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Homework answers / question archive / University of Tech - Iraq - QMDS 10110 CHAPTER 10: TWO-SAMPLE TESTS 1)The t test for the difference between the means of 2 independent populations assumes that the respective sample sizes are equal

University of Tech - Iraq - QMDS 10110 CHAPTER 10: TWO-SAMPLE TESTS 1)The t test for the difference between the means of 2 independent populations assumes that the respective sample sizes are equal

Statistics

University of Tech - Iraq - QMDS 10110

CHAPTER 10: TWO-SAMPLE TESTS

1)The t test for the difference between the means of 2 independent populations assumes that the respective

    1. sample sizes are equal.
    2. sample variances are equal.
    3. populations are approximately normal.
    4. All of the above.

 

 

  1. The t test for the mean difference between 2 related populations assumes that the
    1. population sizes are equal.
    2. sample variances are equal.
    3. population of differences is approximately normal or sample sizes are large enough.
    4. All of the above.

 

 

 

  1. If we are testing for the difference between the means of 2 related populations with samples of n1 = 20 and n2 = 20, the number of degrees of freedom is equal to
    1. 39.
    2. 38.
    3. 19.
    4. 18.

 

 

 

 

  1. If we are testing for the difference between the means of 2 independent populations presumes equal variances with samples of n1 = 20 and n2 = 20, the number of degrees of freedom is equal to
    1. 39.
    2. 38.
    3. 19.
    4. 18.

 

 

 

  1. In what type of test is the variable of interest the difference between the values of the observations rather than the observations themselves?
    1. A test for the equality of variances from 2 independent populations.
    2. A test for the difference between the means of 2 related populations.
    3. A test for the difference between the means of 2 independent populations.
    4. All of the above.

 

 

 

  1. In testing for the differences between the means of 2 independent populations where the variances in each population are unknown but assumed equal, the degrees of freedom are
    1. n – 1.
    2. n1 + n2 – 1.
    3. n1 + n2 – 2.
    4. n – 2.

 

 

 

  1. In testing for differences between the means of 2 related populations where the variance of the differences is unknown, the degrees of freedom are
    1. n – 1.
    2. n1 + n2 – 1.
    3. n1 + n2 – 2.
    4. n – 2.

 

 

 

  1. In testing for differences between the means of two related populations, the null hypothesis is
    1. .
    2. .
    3. .
    4. .

 

 

  1. In testing for differences between the means of two independent populations, the null hypothesis is:
    1.  = 2.
    2.  = 0.
    3.  > 0.
    4.  < 2.

 

 

 

  1. When testing for the difference between 2 population variances with sample sizes of n1 = 8 and n2 = 10, the number of degrees of freedom are
    1. 8 and 10.
    2. 7 and 9.
    3. 18.
    4. 16.

 

 

 

  1. The statistical distribution used for testing the difference between two population variances is the ___ distribution.
    1. t
    2. standardized normal
    3. binomial
    4. F

 

 

 

  1. The test for the equality of two population variances is based on
    1. the difference between the 2 sample variances.
    2. the ratio of the 2 sample variances.
    3. the difference between the 2 population variances.
    4. the difference between the sample variances divided by the difference between the sample means.

 

 

 

  1.  True or False: The F test used for testing the difference in two population variances is always a one-tailed test.

 

 

 

  1. In testing for the differences between the means of two related populations, the _______ hypothesis is the hypothesis of "no differences."

 

  1. In testing for the differences between the means of two related populations, we assume that the differences follow a _______ distribution.

 

 

  1. In testing for the differences between the means of two independent populations, we assume that the 2 populations each follow a _______ distribution.

 

 

  1.  Given the following information, calculate the degrees of freedom that should be used in the pooled-variance t test.

s12 = 4  s22 = 6

n1 = 16 n2 = 25

    1. df = 41
    2. df = 39
    3. df = 16
    4. df = 25

 

 

 

  1. Given the following information, calculate sp2, the pooled sample variance that should be used in the pooled-variance t test.

s12 = 4  s22 = 6

n1 = 16 n2 = 25

    1. sp2 = 6.00
    2. sp2 = 5.00
    3. sp2 = 5.23
    4. sp2 = 4.00

 

 

 

 

TABLE 10-1

 

Are Japanese managers more motivated than American managers? A randomly selected group of each were administered the Sarnoff Survey of Attitudes Toward Life (SSATL), which measures motivation for upward mobility. The SSATL scores are summarized below.

 

 

American

Japanese

Sample Size

211

100

Mean SSATL Score

65.75

79.83

Population Std. Dev.

11.07

6.41

 

  1. Referring to Table 10-1, judging from the way the data were collected, which test would likely be most appropriate to employ?
    1. Paired t test
    2. Pooled-variance t test for the difference between two means
    3. Independent samples Z test for the difference between two means
    4. Related samples Z test for the mean difference

 

 

 

 

  1. Referring to Table 10-1, give the null and alternative hypotheses to determine if the average SSATL score of Japanese managers differs from the average SSATL score of American managers.

 

 

 

  1. Referring to Table 10-1, assuming the independent samples procedure was used, calculate the value of the test statistic.

 

 

 

 

  1. Referring to Table 10-1, suppose that the test statistic is Z = 2.45. Find the p-value if we assume that the alternative hypothesis was a two-tailed test ().
    1. 0.0071
    2. 0.0142
    3. 0.4929
    4. 0.9858

 

 

 

 

 

 

TABLE 10-2

 

A researcher randomly sampled 30 graduates of an MBA program and recorded data concerning their starting salaries. Of primary interest to the researcher was the effect of gender on starting salaries. Analysis of the mean salaries of the females and males in the sample is given below.

 

Hypothesized Difference

0

Level of Significance

0.05

Population 1 Sample

Sample Size

18

Sample Mean

48266.7

Sample Standard Deviation

13577.63

Population 2 Sample

Sample Size

12

Sample Mean

55000

Sample Standard Deviation

11741.29

Difference in Sample Means

-6733.3

t-Test Statistic

-1.40193

Lower-Tail Test

Lower Critical Value

-1.70113

p-Value

0.085962

           

  1. Referring to Table 10-2, the researcher was attempting to show statistically that the female MBA graduates have a significantly lower mean starting salary than the male MBA graduates.  According to the test run, which of the following is an appropriate alternative hypothesis?

 

 

 

  1. Referring to Table 10-2, the researcher was attempting to show statistically that the female MBA graduates have a significantly lower mean starting salary than the male MBA graduates. From the analysis in Table 10-2, the correct test statistic is:
    1. 0.0860
    2. – 1.4019
    3. – 1.7011
    4. – 6,733.33

 

 

 

  1. Referring to Table 10-2, the researcher was attempting to show statistically that the female MBA graduates have a significantly lower mean starting salary than the male MBA graduates. The proper conclusion for this test is:
    1. At the  = 0.10 level, there is sufficient evidence to indicate a difference in the mean starting salaries of male and female MBA graduates.
    2. At the  = 0.10 level, there is sufficient evidence to indicate that females have a lower mean starting salary than male MBA graduates.
    3. At the  = 0.10 level, there is sufficient evidence to indicate that females have a higher mean starting salary than male MBA graduates.
    4. At the  = 0.10 level, there is insufficient evidence to indicate any difference in the mean starting salaries of male and female MBA graduates.

 

 

 

 

  1. Referring to Table 10-2, the researcher was attempting to show statistically that the female MBA graduates have a significantly lower mean starting salary than the male MBA graduates. What assumptions were necessary to conduct this hypothesis test?
    1. Both populations of salaries (male and female) must have approximate normal distributions.
    2. The population variances are approximately equal.
    3. The samples were randomly and independently selected.
    4. All of the above assumptions were necessary.

 

 

 

  1. Referring to Table 10-2, what is the 99% confidence interval estimate for the difference between two means?

 

 

  1. Referring to Table 10-2, what is the 95% confidence interval estimate for the difference between two means?

 

 

  1. Referring to Table 10-2, what is the 90% confidence interval estimate for the difference between two means?

 

 

 

 

 

TABLE 10-3

 

The use of preservatives by food processors has become a controversial issue. Suppose 2 preservatives are extensively tested and determined safe for use in meats. A processor wants to compare the preservatives for their effects on retarding spoilage. Suppose 15 cuts of fresh meat are treated with preservative A and 15 are treated with preservative B, and the number of hours until spoilage begins is recorded for each of the 30 cuts of meat. The results are summarized in the table below.

      Preservative A                   Preservative B

      A = 106.4 hours              B = 96.54 hours

            S A = 10.3 hours                 S B = 13.4 hours

 

  1. Referring to Table 10-3, state the test statistic for determining if the population variances differ for preservatives A and B.
    1. F = – 3.10
    2. F = 0.5908
    3. F = 0.7687
    4. F = 0.8250

 

 

 

  1. Referring to Table 10-3, what assumptions are necessary for a comparison of the population variances to be valid?
    1. Both sampled populations are normally distributed.
    2. Both samples are random and independent.
    3. Neither (a) nor (b) is necessary.
    4. Both (a) and (b) are necessary.

 

 

 

 

 

 

 

 

 

 

 

 

TABLE 10-4

 

A real estate company is interested in testing whether, on average, families in Gotham have been living in their current homes for less time than families in Metropolis have. Assume that the two population variances are equal.  A random sample of 100 families from Gotham and a random sample of 150 families in Metropolis yield the following data on length of residence in current homes.

Gotham:   G = 35 months,                       sG2 = 900       Metropolis:          M = 50 months,     sM2 = 1050

 

  1. Referring to Table 10-4, which of the following represents the relevant hypotheses tested by the real estate company?

 

 

 

 

  1. Referring to Table 10-4, what is the estimated standard error of the difference between the 2 sample means?
    1. 4.06
    2. 5.61
    3. 8.01
    4. 16.00

 

 

 

  1. Referring to Table 10-4, what is an unbiased point estimate for the mean of the sampling distribution of the difference between the 2 sample means?
    1. – 22
    2. – 10
    3. – 15
    4. 0

 

 

 

  1. Referring to Table 10-4, what is(are) the critical value(s) of the relevant hypothesis test if the level of significance is 0.05?
    1. t @ Z = – 1.645
    2. t @ Z = 1.96
    3. t @ Z = – 1.96
    4. t @ Z = – 2.080

 

 

 

  1. Referring to Table 10-4, what is(are) the critical value(s) of the relevant hypothesis test if the level of significance is 0.01?
    1. t @ Z = – 1.96
    2. t @ Z = 1.96
    3. t @ Z = – 2.080
    4. t @ Z = – 2.33

 

 

 

  1. Referring to Table 10-4, what is the standardized value of the estimate of the mean of the sampling distribution of the difference between sample means?
    1. – 8.75
    2. – 3.69
    3. – 2.33
    4. – 1.96

 

 

 

  1. Referring to Table 10-4, suppose  = 0.10. Which of the following represents the result of the relevant hypothesis test?
    1. The alternative hypothesis is rejected.
    2. The null hypothesis is rejected.
    3. The null hypothesis is not rejected.
    4. Insufficient information exists on which to make a decision.

 

 

  1. Referring to Table 10-4, suppose  = 0.05. Which of the following represents the result of the relevant hypothesis test?
    1. The alternative hypothesis is rejected.
    2. The null hypothesis is rejected.
    3. The null hypothesis is not rejected.
    4. Insufficient information exists on which to make a decision.

 

 

 

  1. Referring to Table 10-4, suppose  = 0.01. Which of the following represents the result of the relevant hypothesis test?
    1. The alternative hypothesis is rejected.
    2. The null hypothesis is rejected.
    3. The null hypothesis is not rejected.
    4. Insufficient information exists on which to make a decision.

 

 

 

  1. Referring to Table 10-4, suppose  = 0.1. Which of the following represents the correct conclusion?
    1. There is not enough evidence that, on average, families in Gotham have been living in their current homes for less time than families in Metropolis have.
    2. There is enough evidence that, on average, families in Gotham have been living in their current homes for less time than families in Metropolis have.
    3. There is not enough evidence that, on average, families in Gotham have been living in their current homes for no less time than families in Metropolis have.
    4. There is enough evidence that, on average, families in Gotham have been living in their current homes for no less time than families in Metropolis have.

 

 

 

  1. Referring to Table 10-4, suppose  = 0.05. Which of the following represents the correct conclusion?
    1. There is not enough evidence that, on average, families in Gotham have been living in their current homes for less time than families in Metropolis have.
    2. There is enough evidence that, on average, families in Gotham have been living in their current homes for less time than families in Metropolis have.
    3. There is not enough evidence that, on average, families in Gotham have been living in their current homes for no less time than families in Metropolis have.
    4. There is enough evidence that, on average, families in Gotham have been living in their current homes for no less time than families in Metropolis have.

 

 

 

  1. Referring to Table 10-4, suppose  = 0.01. Which of the following represents the correct conclusion?
    1. There is not enough evidence that, on average, families in Gotham have been living in their current homes for less time than families in Metropolis have.
    2. There is enough evidence that, on average, families in Gotham have been living in their current homes for less time than families in Metropolis have.
    3. There is not enough evidence that, on average, families in Gotham have been living in their current homes for no less time than families in Metropolis have.
    4. There is enough evidence that, on average, families in Gotham have been living in their current homes for no less time than families in Metropolis have.

 

 

 

  1. Referring to Table 10-4, what is the 99% confidence interval estimate for the difference in the two means?

 

 

  1. Referring to Table 10-4, what is the 95% confidence interval estimate for the difference in the two means?

 

 

 

 

TABLE 10-5

 

To test the effectiveness of a business school preparation course, 8 students took a general business test before and after the course. The results are given below.

                       Exam Score                Exam Score

Student                                       Before Course (1)          After Course (2)

1                     530                             670

2                     690                             770

3                     910                          1,000

4                     700                             710

5                     450                             550

6                     820                             870

7                     820                             770

8                     630                             610

 

  1. Referring to Table 10-5, the number of degrees of freedom is
    1. 14.
    2. 13.
    3. 8.
    4. 7.

 

 

 

  1. Referring to Table 10-5, the value of the sample mean difference is _______ if the difference scores reflect the results of the exam after the course minus the results of the exam before the course.
    1. 0
    2. 50
    3. 68
    4. 400

 

 

 

  1. Referring to Table 10-5, the value of the standard error of the difference scores is
    1. 65.027
    2. 60.828
    3. 22.991
    4. 14.696

 

 

 

  1. Referring to Table 10-5, what is the critical value for testing at the 5% level of significance whether the business school preparation course is effective in improving exam scores?
    1. 2.365
    2. 2.145
    3. 1.761
    4. 1.895

 

 

 

  1. Referring to Table 10-5, at the 0.05 level of significance, the decision for this hypothesis test would be:
    1. reject the null hypothesis.
    2. do not reject the null hypothesis.
    3. reject the alternative hypothesis.
    4. It cannot be determined from the information given.

 

 

 

  1. Referring to Table 10-5, at the 0.05 level of significance, the conclusion for this hypothesis test would be:
    1. the business school preparation course does improve exam score.
    2. the business school preparation course does not improve exam score.
    3. the business school preparation course has no impact on exam score.
    4. It cannot be drawn from the information given.

 

 

 

 

  1. True or False:  Referring to Table 10-5, one must assume that the population of difference scores is normally distributed.

 

 

 

 

  1. Referring to Table 10-5, the calculated value of the test statistic is ________.

 

 

  1. Referring to Table 10-5, the p-value of the test statistic is ________.

 

 

 

 

  1. True or False: Referring to Table 10-5, in examining the differences between related samples we are essentially sampling from an underlying population of difference "scores."

 

 

 

  1. True or False: The sample size in each independent sample must be the same if we are to test for differences between the means of 2 independent populations.

 

 

 

  1. True or False: When we test for differences between the means of 2 independent populations, we can only use a two-tailed test.

 

 

 

  1. True or False: When testing for differences between the means of 2 related populations, we can use either a one-tailed or two-tailed test.

 

 

 

  1. True or False: Repeated measurements from the same individuals is an example of data collected from 2 related populations.

 

 

 

  1. True or False: The test for the equality of 2 population variances assumes that each of the 2 populations is normally distributed.

 

 

 

  1. True or False: For all two-sample tests, the sample sizes must be equal in the 2 groups.

 

 

 

  1. True or False: When the sample sizes are equal, the pooled variance of the 2 groups is the average of the 2 sample variances.

 

 

 

  1. True or False: The F distribution is symmetric.

 

 

 

  1. True or False: The F distribution can only have positive values.

 

 

 

  1. True or False: All F tests are one-tailed tests.

 

 

 

  1. True of False: When performing a two-tailed test, the lower-tailed critical value of the F distribution with  degrees of freedom in the numerator and  degrees of freedom in the denominator is exactly equivalent to the reciprocal of the upper-tailed critical value of the F distribution with  degrees of freedom in the numerator and  degrees of freedom in the denominator.

 

 

 

  1. Given the upper-tailed critical value of an F test with 3 degrees of freedom in the numerator and 8 degrees of freedom in the denominator being 4.07, the lower-tailed critical value of an F test with 8 degrees of freedom in the numerator and 3 degrees of freedom in the denominator for the same level of significance will be _________.

 

 

 

  1. True or False: A researcher is curious about the effect of sleep on students’ test performances. He chooses 60 students and gives each 2 tests: one given after 2 hours’ sleep and one after 8 hours’ sleep. The test the researcher should use would be a related samples test.

 

 

 

  1. When testing , the observed value of the Z-score was found to be – 2.13. The p-value for this test would be
    1. 0.0166.
    2. 0.0332.
    3. 0.9668.
    4. 0.9834.

 

 

 

  1. When testing  versus , the observed value of the Z-score was found to be – 2.13. The p-value for this test would be
    1. 0.0166.
    2. 0.0332.
    3. 0.9668.
    4. 0.9834.

 

 

 

  1. When testing  versus , the observed value of the Z-score was found to be – 2.13. The p-value for this test would be
    1. 0.0166.
    2. 0.0332.
    3. 0.9668.
    4. 0.9834.

 

 

 

  1. True or False: A statistics professor wanted to test whether the grades on a statistics test were the same for upper and lower classmen. The professor took a random sample of size 10 from each, conducted a test and found out that the variances were equal. For this situation, the professor should use a t test with related samples.

 

 

 

  1. True or False: A statistics professor wanted to test whether the grades on a statistics test were the same for upper and lower classmen. The professor took a random sample of size 10 from each, conducted a test and found out that the variances were equal. For this situation, the professor should use a t test with independent samples.

 

 

 

  1. True or False: A Marine drill instructor recorded the time in which each of 11 recruits completed an obstacle course both before and after basic training. To test whether any improvement occurred, the instructor would use a t-distribution with 11 degrees of freedom.

 

 

 

  1. True or False: A Marine drill instructor recorded the time in which each of 11 recruits completed an obstacle course both before and after basic training. To test whether any improvement occurred, the instructor would use a t-distribution with 10 degrees of freedom.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

TABLE 10-6

 

Two samples each of size 25 are taken from independent populations assumed to be normally distributed with equal variances.  The first sample has a mean of 35.5 and standard deviation of 3.0 while the second sample has a mean of 33.0 and standard deviation of 4.0.

 

  1. Referring to Table 10-6, the pooled (i.e., combined) variance is _______.

 

 

  1. Referring to Table 10-6, the computed t statistic is _______.

 

 

  1. Referring to Table 10-6, there are _______ degrees of freedom for this test.

 

 

  1. Referring to Table 10-6, the critical values for a two-tailed test of the null hypothesis of no difference in the population means at the  = 0.05 level of significance are _______.

 

 

  1. Referring to Table 10-6, a two-tailed test of the null hypothesis of no difference would _______ (be rejected/not be rejected) at the  = 0.05 level of significance.

 

 

  1. Referring to Table 10-6, the p-value for a two-tailed test whose computed t statistic is 2.50 is between _____ and _______ .

 

 

  1. Referring to Table 10-6, if we were interested in testing against the one-tailed alternative that  at the  = 0.01 level of significance, the null hypothesis would _______ .

 

 

  1. Referring to Table 10-6, the p-value for a one-tailed test whose computed statistic is 2.50 (in the hypothesized direction) is between _______ . 

 

 

  1. Referring to Table 10-6, what is the 99% confidence interval estimate for the difference in the two means?

 

 

  1. Referring to Table 10-6, what is the 95% confidence interval estimate for the difference in the two means?

 

 

  1. Referring to Table 10-6, what is the 90% confidence interval estimate for the difference in the two means?

 

 

 

 

 

 

 

 

 

 

 

 

 

TABLE 10-7

 

To investigate the efficacy of a diet, a random sample of 16 male patients is drawn from a population of adult males using the diet. The weight of each individual in the sample is taken at the start of the diet and at a medical follow-up 4 weeks later.  Assuming that the population of differences in weight before versus after the diet follow a normal distribution, the t-test for related samples can be used to determine if there was a significant decrease in the mean weight during this period.  Suppose the mean decrease in weights over all 16 subjects in the study is 3.0 pounds with the standard deviation of differences computed as 6.0 pounds.

 

  1. Referring to Table 10-7, the t test should be _______-tailed.

 

 

  1. Referring to Table 10-7, the computed t statistic is _______.

 

 

  1. Referring to Table 10-7, there are _______ degrees of freedom for this test.

 

 

  1. Referring to Table 10-7, the critical value for a one-tailed test of the null hypothesis of no difference at the  = 0.05 level of significance is _______.

 

 

  1. Referring to Table 10-7, a one-tailed test of the null hypothesis of no difference would _______ (be rejected/not be rejected) at the  = 0.05 level of significance.

 

 

 

  1. Referring to Table 10-7, the p-value for a one-tailed test whose computed t statistic is 2.00 is between _______.

 

 

  1. Referring to Table 10-7, if we were interested in testing against the two-tailed alternative that  is not equal to zero at the  = 0.05 level of significance, the null hypothesis would _______ (be rejected/not be rejected).

 

 

  1. Referring to Table 10-7, the p-value for a two-tailed test whose computed statistic is 2.00 is between ________ .

 

 

  1. Referring to Table 10-7, what is the 95% confidence interval estimate for the mean difference in weight before and after the diet?

 

 

  1. Referring to Table 10-7, what is the 99% confidence interval estimate for the mean difference in weight before and after the diet?

 

 

  1. Referring to Table 10-7, what is the 90% confidence interval estimate for the mean difference in weight before and after the diet?

 

 

 

 

 

 

 

 

 

 

 

TABLE 10-8

 

A buyer for a manufacturing plant suspects that his primary supplier of raw materials is overcharging. In order to determine if his suspicion is correct, he contacts a second supplier and asks for the prices on various identical materials. He wants to compare these prices with those of his primary supplier. The data collected is presented in the table below, with some summary statistics presented (all of these might not be necessary to answer the questions which follow). The buyer believes that the differences are normally distributed and will use this sample to perform an appropriate test at a level of significance of 0.01.

                              Primary       Secondary

Material          Supplier        Supplier        Difference

             1                  $55               $45                  $10

             2                  $48               $47                    $1

             3                  $31               $32                 – $1

             4                  $83               $77                    $6

             5                  $37               $37                    $0

             6                  $55               $54                    $1     

Sum:                 $309             $292                  $17

Sum of Squares:               $17,573           $15,472            $139

 

  1. Referring to Table 10-8, the hypotheses that the buyer should test are a null hypothesis that ________ versus an alternative hypothesis that ________.

 

 

  1. Referring to Table 10-8, the test to perform is a
    1. pooled-variance t test for differences between two means.
    2. separate-variance t test for differences between two means.
    3. Z test for the difference between two means.
    4. paired t-test for the mean difference.

 

 

 

  1. Referring to Table 10-8, the decision rule is to reject the null hypothesis if ________.

 

 

  1. Referring to Table 10-8, the calculated value of the test statistic is ________.

 

 

  1. Referring to Table 10-8, the p-value of the test is between ________ and ________.

 

 

  1. True or False: Referring to Table 10-8, the null hypothesis should be rejected.

 

 

 

  1. Referring to Table 10-8, the buyer should decide that the primary supplier is
    1. overcharging because there is strong evidence that this is the case.
    2. overcharging because there is insufficient evidence to prove otherwise.
    3. not overcharging because there is insufficient evidence to prove otherwise.
    4. not overcharging because there is strong evidence to prove otherwise.

 

 

 

  1. Referring to Table 10-8, if the buyer had decided to perform a two-tailed test, the p-value would have been between ________ and ________.

 

 

  1. Referring to Table 10-8, what is the 99% confidence interval estimate for the mean difference in prices?

 

 

  1. Referring to Table 10-8, what is the 95% confidence interval estimate for the mean difference in prices?

 

 

  1. Referring to Table 10-8, what is the 90% confidence interval estimate for the mean difference in prices?

 

  1. If we wish to determine whether there is evidence that the proportion of successes is higher in group 1 than in group 2, the appropriate test to use is
    1. the Z test for the difference between two proportions.
    2. the F test for the difference between two variances.
    3. the pooled-variance t test for the difference between two proportions.
    4. the F test for the difference between two proportions.

 

 

 

  1. Moving companies are required by the government to publish a Carrier Performance Report each year. One of the descriptive statistics they must include is the annual percentage of shipments on which a $50 or greater claim for loss or damage was filed. Suppose two companies, Econo-Move and On-the-Move, each decide to estimate this figure by sampling their records, and they report the data shown in the following table.

 

 

Econo-Move

On-the-Move

 

Total shipments sampled

900

750

Number of shipments with a claim  $50

162

60

 

The owner of On-the-Move is hoping to use these data to show that the company is superior to Econo-Move with regard to the percentage of claims filed. Which test would be used to properly analyze the data in this experiment?

  1. Z test for the difference between two means
  2. F test for the difference between two variances
  3. Separate variance t test for the difference between two means
  4. Z test for the difference between two proportions

 

 

 

  1. The Wall Street Journal recently ran an article indicating differences in perception of sexual harassment on the job between men and women. The article claimed that women perceived the problem to be much more prevalent than did men. One question asked of both men and women was: “Do you think sexual harassment is a major problem in the American workplace?” Some 24% of the men compared to 62% of the women responded “Yes.” Assuming W designates women’s responses and M designates men’s, what hypothesis should The Wall Street Journal test in order to show that its claim is true?
  1. H0:   0 versus H1: < 0
  2. H0:  0 versus H1: > 0
  3. H0: = 0 versus H1:  0
  4. H0:  0 versus H1: > 0

 

 

 

  1. The Wall Street Journal recently ran an article indicating differences in perception of sexual harassment on the job between men and women. The article claimed that women perceived the problem to be much more prevalent than did men. One question asked to both men and women was: “Do you think sexual harassment is a major problem in the American workplace?” Some 24% of the men compared to 62% of the women responded “Yes.” Suppose that 150 women and 200 men were interviewed. For a 0.01 level of significance, what is the critical value for the rejection region?
  1. 7.173
  2. 7.106
  3. 6.635
  4. 2.33

 

 

 

  1. The Wall Street Journal recently ran an article indicating differences in perception of sexual harassment on the job between men and women. The article claimed that women perceived the problem to be much more prevalent than did men. One question asked to both men and women was: “Do you think sexual harassment is a major problem in the American workplace?” Some 24% of the men compared to 62% of the women responded “Yes.” Suppose that 150 women and 200 men were interviewed. What is the value of the test statistic?
  1. 7.173
  2. 7.106
  3. 6.635
  4. 2.33    

 

 

  1. The Wall Street Journal recently ran an article indicating differences in perception of sexual harassment on the job between men and women. The article claimed that women perceived the problem to be much more prevalent than did men. One question asked to both men and women was: “Do you think sexual harassment is a major problem in the American workplace?” Some 24% of the men compared to 62% of the women responded “Yes.” Suppose that 150 women and 200 men were interviewed.  Construct a 99% confidence interval estimate of the difference between the proportion of women and men who think sexual harassment is a major problem in the American workplace.

 

 

  1. The Wall Street Journal recently ran an article indicating differences in perception of sexual harassment on the job between men and women. The article claimed that women perceived the problem to be much more prevalent than did men. One question asked to both men and women was: “Do you think sexual harassment is a major problem in the American workplace?” Some 24% of the men compared to 62% of the women responded “Yes.” Suppose that 150 women and 200 men were interviewed.  Construct a 95% confidence interval estimate of the difference between the proportion of women and men who think sexual harassment is a major problem in the American workplace.

 

 

  1. The Wall Street Journal recently ran an article indicating differences in perception of sexual harassment on the job between men and women. The article claimed that women perceived the problem to be much more prevalent than did men. One question asked to both men and women was: “Do you think sexual harassment is a major problem in the American workplace?” Some 24% of the men compared to 62% of the women responded “Yes.” Suppose that 150 women and 200 men were interviewed.  Construct a 90% confidence interval estimate of the difference between the proportion of women and men who think sexual harassment is a major problem in the American workplace.

 

 

  1. The Wall Street Journal recently ran an article indicating differences in perception of sexual harassment on the job between men and women. The article claimed that women perceived the problem to be much more prevalent than did men. One question asked to both men and women was: “Do you think sexual harassment is a major problem in the American workplace?” Some 24% of the men compared to 62% of the women responded “Yes.” Suppose that 150 women and 200 men were interviewed. What conclusion should be reached?
  1. Using a 0.01 level of significance, there is sufficient evidence to conclude that women perceive the problem of sexual harassment on the job as much more prevalent than do men.
  2. There is insufficient evidence to conclude with at least 99% confidence that women perceive the problem of sexual harassment on the job as much more prevalent than do men.
  3. There is no evidence of a significant difference between the men and women in their perception.
  4. More information is needed to draw any conclusions from the data set.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

  1. A powerful women’s group has claimed that men and women differ in attitudes about sexual discrimination. A group of 50 men (group 1) and 40 women (group 2) were asked if they thought sexual discrimination is a problem in the United States. Of those sampled, 11 of the men and 19 of the women did believe that sexual discrimination is a problem. Assuming W designates women’s responses and M designates men’s, which of the following are the appropriate null and alternative hypotheses to test the group’s claim?
  1. H0:   0 versus H1: < 0
  2. H0:  0 versus H1: > 0
  3. H0: = 0 versus H1:  0
  4. H0:  0 versus H1: = 0

 

 

 

  1. A powerful women’s group has claimed that men and women differ in attitudes about sexual discrimination. A group of 50 men (group 1) and 40 women (group 2) were asked if they thought sexual discrimination is a problem in the United States. Of those sampled, 11 of the men and 19 of the women did believe that sexual discrimination is a problem. Find the value of the test statistic.
  1. Z = – 2.55
  2. Z = – 0.85
  3. Z = – 1.05
  4. Z = – 1.20

 

 

 

  1. A powerful women’s group has claimed that men and women differ in attitudes about sexual discrimination. A group of 50 men (group 1) and 40 women (group 2) were asked if they thought sexual discrimination is a problem in the United States. Of those sampled, 11 of the men and 19 of the women did believe that sexual discrimination is a problem. If the p-value turns out to be 0.035 (which is not the real value in this data set), then
    1. at  = 0.05, we should fail to reject H0
    2. at  = 0.04, we should reject H0
    3. at  = 0.03, we should reject H0
    4. None of the above would be correct statements.

 

 

 

  1. A powerful women’s group has claimed that men and women differ in attitudes about sexual discrimination. A group of 50 men (group 1) and 40 women (group 2) were asked if they thought sexual discrimination is a problem in the United States. Of those sampled, 11 of the men and 19 of the women did believe that sexual discrimination is a problem.  Construct a 99% confidence interval estimate of the difference between the proportion of men and women who believe that sexual discrimination is a problem.

 

 

  1. A powerful women’s group has claimed that men and women differ in attitudes about sexual discrimination. A group of 50 men (group 1) and 40 women (group 2) were asked if they thought sexual discrimination is a problem in the United States. Of those sampled, 11 of the men and 19 of the women did believe that sexual discrimination is a problem.  Construct a 95% confidence interval estimate of the difference between the proportion of men and women who believe that sexual discrimination is a problem.

 

 

  1. A powerful women’s group has claimed that men and women differ in attitudes about sexual discrimination. A group of 50 men (group 1) and 40 women (group 2) were asked if they thought sexual discrimination is a problem in the United States. Of those sampled, 11 of the men and 19 of the women did believe that sexual discrimination is a problem.  Construct a 90% confidence interval estimate of the difference between the proportion of men and women who believe that sexual discrimination is a problem.

 

TABLE 10-9

 

A few years ago, Pepsi invited consumers to take the “Pepsi Challenge.” Consumers were asked to decide which of two sodas, Coke or Pepsi, they preferred in a blind taste test. Pepsi was interesting in determining what factors played a role in people’s taste preferences. One of the factors studied was the gender of the consumer. Below are the results of analyses comparing the taste preferences of men and women with the proportions depicting preference for Pepsi.

 

Males: n = 109, pM = 0.422018     Females: n = 52, pF = 0.25

pMpF = 0.172018                        Z = 2.11825

 

  1. Referring to Table 10-9, to determine if a difference exists in the taste preferences of men and women, give the correct alternative hypothesis that Pepsi would test.
  1. H1:
  2. H1:
  3. H1:   0
  4. H1: = 0

 

 

 

  1. Referring to Table 10-9, suppose Pepsi wanted to test to determine if the males preferred Pepsi more than the females. Using the test statistic given, compute the appropriate p-value for the test.
  1. 0.0171
  2. 0.0340
  3. 0.2119
  4. 0.4681

 

 

 

  1. Referring to Table 10-9, suppose Pepsi wanted to test to determine if the males preferred Pepsi less than the females. Using the test statistic given, compute the appropriate p-value for the test.
  1. 0.0170
  2. 0.0340
  3. 0.9660
  4. 0.9830

 

 

 

  1. Referring to Table 10-9, suppose that the two-tailed p-value was really 0.0734. State the proper conclusion.
  1. At  = 0.05, there is sufficient evidence to indicate the proportion of males preferring Pepsi differs from the proportion of females preferring Pepsi.
  2. At  = 0.10, there is sufficient evidence to indicate the proportion of males preferring Pepsi differs from the proportion of females preferring Pepsi.
  3. At  = 0.05, there is sufficient evidence to indicate the proportion of males preferring Pepsi equals the proportion of females preferring Pepsi.
  4. At  = 0.08, there is insufficient evidence to indicate the proportion of males preferring Pepsi differs from the proportion of females preferring Pepsi.

 

 

 

  1. Referring to Table 10-9, construct a 90% confidence interval estimate of the difference between the proportion of males and females who prefer Pepsi.

 

 

  1. Referring to Table 10-9, construct a 95% confidence interval estimate of the difference between the proportion of males and females who prefer Pepsi.

 

 

  1. Referring to Table 10-9, construct a 99% confidence interval estimate of the difference between the proportion of males and females who prefer Pepsi.

 

 

 

 

TABLE 10-10

 

The following EXCEL output contains the results of a test to determine if the proportions of satisfied guests at two resorts are the same or different. 

 

Hypothesized Difference

0

Level of Significance

0.05

Group 1

Number of Successes

163

Sample Size

227

Group 2

Number of Successes

154

Sample Size

262

Group 1 Proportion

0.718061674

Group 2 Proportion

0.58778626

Difference in Two Proportions

0.130275414

Average Proportion

0.648261759

Test Statistic

3.00875353

Two-Tailed Test

Lower Critical Value

?1.959961082

Upper Critical Value

1.959961082

p-Value

0.002623357

 

  1. Referring to Table 10-10, allowing for 0.75% probability of committing a Type I error, what are the decision and conclusion on testing whether there is any difference in the proportions of satisfied guests in the two resorts?
  1. Do not reject the null hypothesis; there is enough evidence to conclude that there is significant difference in the proportions of satisfied guests at the two resorts.
  2. Do not reject the null hypothesis; there is not enough evidence to conclude that there is significant difference in the proportions of satisfied guests at the two resorts.
  3. Reject the null hypothesis; there is enough evidence to conclude that there is significant difference in the proportions of satisfied guests at the two resorts.
  4. Reject the null hypothesis; there is not enough evidence to conclude that there is significant difference in the proportions of satisfied guests at the two resorts.

 

 

 

 

  1. Referring to Table 10-10, if you want to test the claim that "Resort 1 (Group 1) has a higher proportion of satisfied guests compared to Resort 2 (Group 2)", the p-value of the test will be
  1. 0.00262
  2. 0.00262/2 
  3. 2(0.00262)
  4. 1-(0.00262/2)

 

 

 

 

  1. Referring to Table 10-10, if you want to test the claim that "Resort 1 (Group 1) has a lower proportion of satisfied guests compared to Resort 2 (Group 2)", you will use
  1. a t-test for the difference between two proportions.
  2. a z-test for the difference between two proportions.
  3. an F test for the difference between two proportions.
  4. a  test for the difference between two proportions.

 

 

 

 

  1. Referring to Table 10-10, construct a 99% confidence interval estimate of the difference in the population proportion of satisfied guests between the two resorts.

 

 

  1. Referring to Table 10-10, construct a 95% confidence interval estimate of the difference in the population proportion of satisfied guests between the two resorts.

 

 

  1. Referring to Table 10-10, construct a 90% confidence interval estimate of the difference in the population proportion of satisfied guests between the two resorts.

 

 

TABLE 10-11

 

A corporation randomly selects 150 salespeople and finds that 66% who have never taken a self-improvement course would like such a course. The firm did a similar study 10 years ago in which 60% of a random sample of 160 salespeople wanted a self-improvement course. The groups are assumed to be independent random samples. Let and  represent the true proportion of workers who would like to attend a self-improvement course in the recent study and the past study, respectively.

 

  1. Referring to Table 10-11, if the firm wanted to test whether this proportion has changed from the previous study, which represents the relevant hypotheses?
  1. H0:  = 0 versus H1:  0
  2. H0:  0 versus H1: = 0
  3. H0:  0 versus H1: > 0
  4. H0:  0 versus H1: < 0

 

 

 

  1. Referring to Table 10-11, if the firm wanted to test whether a greater proportion of workers would currently like to attend a self-improvement course than in the past, which represents the relevant hypotheses?
  1. H0: = 0 versus H1:  0
  2. H0:  0 versus H1: = 0
  3. H0:  0 versus H1: > 0
  4. H0:  0 versus H1: < 0

 

 

 

  1. Referring to Table 10-11, what is the unbiased point estimate for the difference between the two population proportions?
  1. 0.06
  2. 0.10
  3. 0.15
  4. 0.22

 

 

 

  1. Referring to Table 10-11, what is/are the critical value(s) when performing a Z test on whether population proportions are different if  = 0.05?
  1.  1.645
  2.  1.96
  3. ?1.96
  4.  2.08

 

 

 

  1. Referring to Table 10-11, what is/are the critical value(s) when testing whether population proportions are different if  = 0.10?
  1.  1.645
  2.  1.96
  3. -1.96
  4.  2.08

 

 

 

  1. Referring to Table 10-11, what is/are the critical value(s) when testing whether the current population proportion is higher than before if  = 0.05?
  1. 1.645
  2. + 1.645
  3. 1.96
  4. + 1.96

 

 

 

  1. Referring to Table 10-11, what is the estimated standard error of the difference between the two sample proportions?
  1. 0.629
  2. 0.500
  3. 0.055
  4. 0

 

 

 

  1. Referring to Table 10-11, what is the value of the test statistic to use in evaluating the alternative hypothesis that there is a difference in the two population proportions?
  1. 4.335
  2. 1.96
  3. 1.093
  4. 0

 

 

 

  1. Referring to Table 10-11, the company tests to determine at the 0.05 level whether the population proportion has changed from the previous study. Which of the following is most correct?
  1. Reject the null hypothesis and conclude that the proportion of employees who are interested in a self-improvement course has changed over the intervening 10 years.
  2. Do not reject the null hypothesis and conclude that the proportion of employees who are interested in a self-improvement course has not changed over the intervening 10 years.
  3. Reject the null hypothesis and conclude that the proportion of employees who are interested in a self-improvement course has increased over the intervening 10 years.
  4. Do not reject the null hypothesis and conclude that the proportion of employees who are interested in a self-improvement course has increased over the intervening 10 years.

 

 

  1. Referring to Table 10-11, construct a 99% confidence interval estimate of the difference in proportion of workers who would like to attend a self-improvement course in the recent study and the past study.

 

 

  1. Referring to Table 10-11, construct a 95% confidence interval estimate of the difference in proportion of workers who would like to attend a self-improvement course in the recent study and the past study.

 

 

  1. Referring to Table 10-11, construct a 90% confidence interval estimate of the difference in proportion of workers who would like to attend a self-improvement course in the recent study and the past study.

 

 

  1. True or False:  In testing the difference between two proportions using the normal distribution, we may use a two-tailed Z test.

 

 

 

  1. If we wish to determine whether there is evidence that the proportion of successes is higher in Group 1 than in Group 2, and the test statistic for Z = +2.07 where the difference is defined as Group 1’s proportion minus Group 2’s proportion, the p-value is equal to ______.

 

 

  1. If we wish to determine whether there is evidence that the proportion of successes is higher in Group 1 than in Group 2, and the test statistic for Z = ?2.07 where the difference is defined as Group 1’s proportion minus Group 2’s proportion, the p-value is equal to ______.

 

 

TABLE 10-12

 

The dean of a college is interested in the proportion of graduates from his college who have a job offer on graduation day. He is particularly interested in seeing if there is a difference in this proportion for accounting and economics majors. In a random sample of 100 of each type of major at graduation, he found that 65 accounting majors and 52 economics majors had job offers. If the accounting majors are designated as “Group 1” and the economics majors are designated as “Group 2,” perform the appropriate hypothesis test using a level of significance of 0.05.

 

  1. Referring to Table 10-12, the hypotheses the dean should use are:
  1. H0:  = 0 versus H1:  0
  2. H0:  0 versus H1: = 0
  3. H0:  0 versus H1: > 0
  4. H0:  0 versus H1: < 0

 

 

  1. Referring to Table 10-12, the null hypothesis will be rejected if the test statistic is ________.

 

 

  1. Referring to Table 10-12, the value of the test statistic is ________.

 

 

  1. Referring to Table 10-12, the p-value of the test is ________.

 

 

  1. True or False: Referring to Table 10-12, the null hypothesis should be rejected.

 

 

 

  1. True or False: Referring to Table 10-12, the same decision would be made with this test if the level of significance had been 0.01 rather than 0.05.

 

 

 

  1. True or False: Referring to Table 10-12, the same decision would be made with this test if the level of significance had been 0.10 rather than 0.05.

 

 

 

  1. Referring to Table 10-12, construct a 99% confidence interval estimate of the difference in proportion between accounting majors and economic majors who have a job offer on graduation day.

 

 

  1. Referring to Table 10-12, construct a 95% confidence interval estimate of the difference in proportion between accounting majors and economic majors who have a job offer on graduation day.

 

 

  1. Referring to Table 10-12, construct a 90% confidence interval estimate of the difference in proportion between accounting majors and economic majors who have a job offer on graduation day.

 

 

 

 

 

TABLE 10-13

 

A quality control engineer is in charge of the manufacture of computer disks. Two different processes can be used to manufacture the disks. He suspects that the Kohler method produces a greater proportion of defects than the Russell method. He samples 150 of the Kohler and 200 of the Russell disks and finds that 27 and 18 of them, respectively, are defective. If Kohler is designated as “Group 1” and Russell is designated as “Group 2,” perform the appropriate test at a level of significance of 0.01.

 

  1. Referring to Table 10-13, the hypotheses that should be tested are:
  1. H0: = 0 versus H1:  0
  2. H0:  0 versus H1: = 0
  3. H0:  0 versus H1: > 0
  4. H0:  0 versus H1: < 0

 

 

  1. Referring to Table 10-13, the null hypothesis will be rejected if the test statistic is ________.

 

 

  1. Referring to Table 10-13, the value of the test statistic is ________.

 

 

  1. Referring to Table 10-13, the p-value of the test is ________.

 

 

  1. True or False: Referring to Table 10-13, the null hypothesis should be rejected.

 

 

  1. True or False: Referring to Table 10-13, the same decision would be made with this test if the level of significance had been 0.05 rather than 0.01.

 

 

  1. True or False: Referring to Table 10-13, the same decision would be made if this had been a two-tailed test at a level of significance of 0.01.

 

 

  1. Referring to Table 10-13, construct a 90% confidence interval estimate of the difference in proportion between the Kohler and Russell disks that are defective.

 

 

  1. Referring to Table 10-13, construct a 95% confidence interval estimate of the difference in proportion between the Kohler and Russell disks that are defective.

 

 

  1. Referring to Table 10-13, construct a 99% confidence interval estimate of the difference in proportion between the Kohler and Russell disks that are defective.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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