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Homework answers / question archive / 1) A difference between calculating the sample mean and the population mean is A) Only in the symbols, we use instead of μ and n instead of N B) We divide the sum of the observations by n - 1 instead of n

1) A difference between calculating the sample mean and the population mean is

A) Only in the symbols, we use instead of μ and n instead of N

B) We divide the sum of the observations by n - 1 instead of n.

C) The observations are ranked and select the middle value for the population mean.

D) There are no differences.

2) Which of the following measures of central location is affected most by extreme values?

A) Median

B) Mean

C) Mode

D) Geometric mean

3) Which level of measurement is required for the median?

A) Nominal

B) Ordinal

C) Interval

D) Ratio

4) Which level of measurement is required for the mode?

A) Nominal

B) Ordinal

C) Interval

D) Ratio

5) In a set of observations, which measure of central tendency reports the value that occurs most often?

A) Mean

B) Median

C) Mode

D) Geometric mean

6) The weighted mean is a special case of the

A) Mean

B) Median

C) Mode

D) Geometric mean

7) The relationship between the geometric mean and the arithmetic mean is

A) They will always be the same.

B) The geometric mean will always be larger.

C) The geometric mean will be equal to or less than the mean.

D) The mean will always be larger than the geometric mean.

8) Suppose you compare the mean of raw data and the mean of the same raw data grouped into a frequency distribution. These two means will be

A) Exactly equal.

B) The same as the median.

C) The same as the geometric mean.

D) Approximately equal.

9) In a set of 10 observations the mean is 20 and the median is 15. There are 2 values that are 6, and all other values are different. What is the mode?

A) 15

B) 20

C) 6

D) None of the above.

10) Which of the measures of central tendency is the largest in a positively skewed distribution?

A) Mean

B) Median

C) Mode

D) Cannot tell from the information given.

11) Which of the following is not a measure of dispersion?

A) Range

B) Variance

C) Standard deviation

D) All of the above are measures of dispersion

12) A disadvantage of the range is

A) Only two values are used in its calculation.

B) It is in different units than the mean.

C) It does not exist for some data sets.

D) All of the above.

13) The mean deviation is

A) Based on squared deviations from the mean.

B) Also called the variance.

C) Based on absolute values.

D) Always reported in squared units.

14) The standard deviation is

A) Based on squared deviations from the mean.

B) In the same units as the mean.

C) Uses all the observations in its calculation.

D) All of the above.

15) The variance is

A) Found by dividing by N by the mean.

B) In the same units as the original data.

C) Found by squaring the standard deviation.

D) All of the above.

16) In a positively skewed distribution

A) The mean, median, and mode are all equal.

B) The mean is larger than the median.

C) The median is larger than the mean.

D) The standard deviation must be larger than the mean or the median.

17) Which of the following statements is true regarding the standard deviation?

A) It cannot assume a negative value.

B) If it is zero, then all the data values are the same.

C) It is in the same units as the mean.

D) All the above are all correct.

18) Under which of the following conditions would the standard deviation assume a negative value.

A) When all the data values were negative.

B) When more than half of the data values were negative.

C) If all the data values were the same.

D) The standard deviation cannot be negative.

19) For a stem-and-leaf display

A) Arrange the leaf values from smallest to largest.

B) Make sure the stem value is only one digit.

C) Do not allow stems with no leaf values.

D) All of the above.

20)Questions 2 to 6 refer to the following information. It reports the number of TV sets sold per day at the Appliance Center.

1 11333

2 6

3 00234

4 555688999

5 1234

6 56788

7

8 8

This arrangement is called a

A) Frequency distribution

B) A frequency polygon

C) A pie chart

D) A stem-and-leaf chart

21) How many days were studied?

A) 11

B) 30

C) 50

D) None of the above

22) What was the smallest and largest number of sets sold per day?

A) 1, 8

B) 10, 80

C) 11,88

D) None of the above

23) How many days were there less than 30 sets sold?

A) 15

B) 6

C) 30

D) None of the above

24) The actual number of sets sold per day between 60 and 69 is

A) 65, 66, 67, 68, 68

B) 60, 69

C) Cannot tell from the information given

D) None of the above

25) The quartile deviation is

A) The square root of the variance.

B) Based on the middle 50 percent of the observations.

C) In squared units of the original data.

D) Appropriate only for symmetric distributions.

26) In a symmetric distribution

A) The mean, median, and mode are equal.

B) The mean is the largest measure of location.

C) The median is the largest measure of location.

D) The standard deviation is the largest value.

27) A coefficient of skewness of -2.73 was computed for a set of data. We conclude that

A) The mean is larger than the median.

B) The median is larger than the mean.

C) The standard deviation is a negative number.

D) Something is wrong because the coefficient of skewness cannot be less than -1.00.

28) A scatter diagram:

A) Is a graphic tool designed to portray the relationship between variables.

B) Uses interval or ratio scale data.

C) Does not allow negative values.

D) Both A and B are correct.

29) Which of the following is a correct statement about a probability?

A) It may range from 0 to 1.

B) It may assume negative values.

C) It may be greater than 1.

D) It cannot be reported to more than 1 decimal place.

30) An experiment is a

A) Collection of events.

B) Collection of outcomes.

C) Always greater than 1.

D) The act of taking a measurement or the observation of some activity.

E) None of the above is correct.

**PART 2**

1) Which of the following is not a type of probability?

A) Subjective

B) Independent

C) Relative frequency

D) Classical

2) Events are independent if

A) By virtue of one event happening another cannot.

B) The probability of their occurrence is greater than 1.

C) We can count the possible outcomes.

D) The probability of one event happening does not affect the probability of another event happening.

E) None of the above.

3) The Special Rule of Addition is used to combine

A) Independent events.

B) Mutually exclusive events

C) Events that total more than one.

D) Events based on subjective probabilities

E) Found by using joint probabilities.

4) We use the General Rule of Multiplication to combine

A) Events that are not independent.

B) Mutually exclusive events.

C) Events that total more than 1.00.

D) Events based on subjective probabilities

E) Found by using joint probabilities.

5) When we find the probability of an event happening by subtracting the probability of the event not happening from 1, we are using

A) Subjective probability

B) The complement rule.

C) The general rule of addition.

D) The special rule of multiplication

E) Joint probability

6) When we determine the number of combinations

A) We are really computing a probability.

B) The order of the outcomes is not important.

C) The order of the outcomes is important.

D) We multiple the likelihood of two independent trials.

E) None of the above.

7) Bayes' Theorem

A) Is an example of subjective probability

B) Can assume of value less than 0.

C) Is used to revise a probability based on new or additional information.

D) Is found by applying the complement rule.

E) None of the above.

8) The difference between a permutation and a combination is:

A) In a permutation order is important and in a combination it is not.

B) In a permutation order is not important and in a combination it is important.

C) A combination is based on the classical definition of probability.

D) A permutation is based on the classical definition of probability.

E) None of the above.

9) The difference between a random variable and a probability distribution is

A) A random variable does not include the probability of an event.

B) A random variable can only assume whole numbers.

C) A probability distribution can only assume whole numbers.

D) None of the above.

10) Which of the following is not a requirement of a binomial distribution?

A) A constant probability of success.

B) Only two possible outcomes.

C) A fixed number of trails.

D) Equally likely outcomes.

11) The mean and the variance are equal in

A) All probability distributions.

B) The binomial distribution.

C) The Poisson distribution.

D) The hypergeometric distribution.

12) In which of the following distributions is the probability of a success usually small?

A) Binomial

B) Poisson

C) Hypergeometric

D) All distribution

13) Which of the following is not a requirement of a probability distribution?

A) Equally likely probability of a success.

B) Sum of the possible outcomes is 1.00.

C) The outcomes are mutually exclusive.

D) The probability of each outcome is between 0 and 1.

14) For a binomial distribution

A) n must assume a number between 1 and 20 or 25.

B) ? must be a multiple of .10.

C) There must be at least 3 possible outcomes.

D) None of the above.

15) Which of the following is a major difference between the binomial and the hypergeometric distributions?

A) The sum of the outcomes can be greater than 1 for the hypergeometric.

B) The probability of a success changes from trial to trial in the hypergeometric distribution.

C) The number of trials changes in the hypergeometric distribution.

D) The outcomes cannot be whole numbers in the hypergeometric distribution.

16) In a continuous probability distribution

A) Only certain outcomes are possible.

B) All the values within a certain range are possible.

C) The sum of the outcomes is greater than 1.00

D) None of the above.

17) For a binomial distribution with n = 15 as ? changes from .50 toward .05 the distribution will

A) Become more positively skewed.

B) Become more negatively skewed

C) Become symmetrical.

D) All of the above.

18) The expected value of the a probability distribution

A) Is the same as the random variable.

B) Is another term for the mean.

C) Is also called the variance.

D) Cannot be greater than 1.

19) The normal distribution is a

A) Discrete distribution

B) Continuous distribution.

C) Positively skewed distribution

D) None of the above.

20) Which of the following are characteristics of the normal distribution?

A) It is a symmetric distribution.

B) It is bell-shaped.

C) It is asymptotic.

D) All of the above.

21) Which of the following are correct statements about a normal distribution?

A) It cannot assume negative numbers.

B) It is defined by its mean and standard deviation.

C) All normal distributions have a variance of at least 1.

D) All of the above are correct.

22) Which of the following statements is correct regarding the standard normal distribution?

A) It is also called the z distribution

B) Any normal distribution can be converted to the standard normal distribution

C) The mean is 0 and the standard deviation is 1.

D) All of the above are correct.

23) The area under a normal curve between 0 and -1.75 is

A) .0401

B) .9599

C) .4599

D) None of the above.

24) The area under a normal curve less than 1.75 is

A) .0401

B) .9599

C) .4599

D) None of the above.

25) The continuity correction factor is used when

A) The sample size is at least 5.

B) Both n? and n(1 - ?) are at least 30.

C) A continuous distribution is used to approximate a discrete distribution.

D) The standard normal distribution is applied.

26) A uniform distribution is defined by

A) Its largest and smallest value.

B) Largest value

C) Smallest value

D) None of the above.

27) The normal approximation to the binomial is used when

A) The sample size is at least 30.

B) Both n? and n(1 - ?) are at least 5.

C) The mean and the variance are the same.

D) The z value is greater than 0.

28) In the standard normal distribution, what is the probability of finding a z value between -1.25 and -1.00?

A) 0.3944

B) 0.3413

C) 0.7357

D) 0.0531

**PART 3**

1) A sample

a. Is a part of the population.

b. Has more than 30 observations.

c. Is usually identified as N.

d. All of the above.

2) Which of the following is not a reason for sampling?

a. The destructive nature of certain tests.

b. The physical impossibility of checking all the items in the population.

c. The adequacy of sample results.

d. All of the above are reasons for sampling.

3) Which of the following is not a method of probability sampling?

a. Random sampling

b. Systematic sampling

c. Stratified sampling

d. All of the above are methods of probability sampling.

4) In a simple random sample

a. Every kth item is selected to be in the sample.

b. Every item has a chance to be in the sample.

c. Every item has the same chance to be in the sample.

d. All of the above.

5) Suppose a population consisted of 20 items. How many different samples of n = 3 are possible?

a. 6840

b. 1140

c. 20

d. 120

6) The difference between the sample mean and the population mean is called the

a. Population mean.

b. Population standard deviation.

c. Standard error of the mean.

d. Sampling error.

7) The mean of the all the sample means and the population mean will

a. Always be equal.

b. Always be normally distributed.

c. Characterized by the standard error of the mean.

d. None of the above.

8) Suppose we have a population that follows the normal distribution. Which of the following statements is correct regarding the distribution of sample means?

a. The population standard deviation is always unknown.

b. The distribution of samples means will follow the uniform distribution.

c. The distribution of the sample means will also follow the normal distribution.

d. None of the above is correct.

9) Suppose we have a population that does not follow the normal distribution. If we select sample of what size will the distribution approximate the normal distribution?

a. 2

b. 5

c. 20

d. 30

10) The standard error of the mean is

a. The standard deviation of the sampling distribution of sample means.

b. Always normally distributed.

c. Sometimes less than 0.

d. None of the above.

11) A point estimate is

a. Always an estimate of the population mean.

b. Always equal to the population value.

c. An estimate of the population parameter.

d. None of the above

12) A confidence interval

a. Always includes the population parameter.

b. Decreases in width as the sample size is increased.

c. Cannot include a value of 0.

d. None of the above.

13) If we wished to decrease the width of a confidence interval, we would not do which of the following.

a. Increase the size of the sample.

b. Reduce the size of the population.

c. Decrease the level of confidence.

d. None of the above.

14) We wish to develop a confidence interval for the population mean. The shape of the population is not known, but we have a sample of 40 observations. We decide to use the 92 percent level of confidence. The appropriate value of z is:

a. 1.96

b. 1.65

c. 2.58

d. 1.75

15) Which of the following statements is not a characteristic of the t distribution?

a. It is a continuous distribution.

b. It has a mean of 0.

c. It is symmetrical.

d. Like z there is only one t distribution.

16) We wish to develop a confidence interval for the population mean. The population follows the normal distribution, the standard deviation of the population is 3, and we have a sample of 10 observations. We decide to use the 90 percent level of confidence. The appropriate value of to represent the level of confidence is

a. z =1.65

b. z = 1.96

c. t = 1.833

d. t = 1.812

17) The fraction or ratio of a sample possessing a certain trait is called a

a. Population.

b. Mean.

c. Confidence interval.

d. Proportion.

18) To develop a confidence interval for a proportion

a. We need to meet the binomial conditions

b. The sample should be at least 100.

c. B should be less than .05.

d. None of the above.

19) The finite population correction factor is used when

a. n is more than 30.

b. N is more than 1000.

c. nB is greater than 5.

d. n/N is more than .05.

20) We wish to estimate the population proportion. We want to be 95 percent confident of our results and we want the estimate to be with .01 of the population parameter. No estimate of the population proportion is available. What value should we use for p?

a. 1.96

b. .01

c. .50

d. We cannot complete the problem, we need more information.

21) The null hypothesis

a. Is a statement about the value of the population parameter.

b. Will always contain the equal sign.

c. Cannot include values less than 0.

d. Both a and b are correct.

22) The alternate hypothesis

a. Is accepted if the null hypothesis is rejected.

b. Will always contain the equal sign.

c. Tells the value of the sample mean.

d. None of the above.

23) The level of significance

a. Is frequently .05 or .01

b. Can be any value between 0 and 1.

c. Is the likelihood of rejecting the null hypothesis when it is true.

d. All of the above.

24) A Type I error is

a. The correct decision

b. A value determined from the test statistic

c. Rejecting the null hypothesis when it is true

d. Accepting the null hypothesis when it is false.

25) The critical value is

a. Calculated from sample information.

b. Cannot be negative.

c. The point that divides the acceptance region from the rejection region.

d. A value determined from the test statistic.

26) In a one-tailed test

a. The rejection region is in only one of the tails.

b. The rejection region is split between the tails.

c. The p-value is always less than the significance level.

d. The p-value is always more than the significance level.

27) To conduct a one sample test of means and use the z distribution as the test statistic

a. We need to know the population mean.

b. We need to know the population standard deviation.

c. We need nπ to be less than 5.

d. Both a and b are correct.

28) A p-value is

a. The same as the population proportion.

b. The same as the significance level.

c. The fraction of the population that has a particular characteristic.

d. The probability of finding a value of the test statistic this extreme when the null hypothesis is true.

29) A Type II error occurs when

a. We accept a false null hypothesis.

b. We reject a true alternate hypothesis.

c. We reject a false null hypothesis.

d. None of the above.

30) Which of the following statements are correct when deciding whether to use the z or the t distribution

a. Use zin a test of proportions when nπ and n(1 - π) are greater than or equal to 5.

b. Use z when we have a normal population and we know the standard deviation.

c. Use t when the population is normal and the population standard deviation is not known

d. All of the above statements are correct.

**PART 4**

1) In a two-sample test of means for independent samples, the equal sign always appears in

a. The null hypothesis.

b. The alternate hypothesis.

c. The upper tail of the test statistic.

d. None of the above.

2) In a two-sample test of means for independent samples, we use the z distribution when

a. The population standard deviations are equal.

b. Both populations have at least 4000 observations.

c. Both population standard deviations are known.

d. nB and n(1-B) are both greater than 5.

3) Which of the following is a requirement for a two-sample test of proportions.

a. The population standard deviations are equal.

b. Both populations are positively skewed.

c. Both samples are at least 30.

d. nB and n(1-B) are both greater than 5.

4) A random sample of 10 observations is selected from the first normal population and 8 from the second normal population. For a one-tailed test of hypothesis (.01 significance level) to determine if there is a difference in the population means, the degrees of freedom are

a. 18

b. 17

c. 16

d. None of the above

5) A random sample of 10 observations is selected from the first normal population and 8 from the second normal population. For a one-tailed test of hypothesis (.01 significance level) to determine if there is a difference in the population means, the critical value(s) are

a. 2.552

b. -2.921, 2.921

c. -2.583, 2.583

d. None of the above

6) Which of the following is not a requirement for the two-sample test of means for independent samples observations?

a. Normal populations

b. Equal population standard deviations

c. Equal sample sizes

d. All of the above are required.

7) To conduct a test of means for two independent samples which of the following are always required?

a. At least one of the samples must have 30 observations.

b. Both samples must have 30 observations.

c. np and n (1 - p) must be 5.

d. None of the above.

8) To conduct a test of hypothesis for dependent samples we assume that

a. The distribution of the difference between the paired observations follows the normal distribution.

b. Both samples are at least 30.

c. The samples are unrelated.

d. All of the above.

9) When conducting a test of hypothesis for the dependent samples

a. We should have at least 30 pairs.

b. The significance level is more than .05.

c. The p-value is more than .10.

d. None of the above

10) Which of the following is not necessary to determine a p-value?

a. Knowledge of whether the test is one-tailed or two-tailed.

b. The value of the test statistic.

c. The level of significance.

d. All of the above.

11) The term ANOVA

a. Has no special meaning.

b. Stands for Analysis of Variance.

c. Stands for Another Numerical Observation of the Variance.

d. None of the above.

12) The general idea of analysis of variance is to compare estimates of variance

a. From both between the treatment means and within the treatment means

b. Based on the several treatments.

c. From within the treatments.

d. None of the above.

13) Which of the following is not a characteristic of the F distribution?

a. It is a discrete distribution.

b. In cannot be negative.

c. It is based on two sets of degrees of freedom.

d. All of the above.

14) The term “Treatment” refers to

a. A source of variation.

b. The numerator degrees of freedom.

c. The variation within the cells.

d. None of the above.

15) Suppose we select 6 observations from each of three treatments. The appropriate degrees of freedom are

a. 3 and 6.

b. 2 and 6.

c. 2 and 15.

d. None of the above

16): The term MSE

a. Is called the mean square error.

b. Is found by SSE/(n - k).

c. Is an estimate of the common population variance.

d. All of the above.

17) Which of the following is not an assumption required for ANOVA?

a. The populations are normally distributed

b. The populations have equal standard deviations

c. The samples are independent.

d. All of the above.

18) Under which of the following conditions will the computed value of F be negative?

a. When there is no difference in the treatment means

b. When there is no difference in the block means

c. When the SS total is larger than SST.

d. F cannot be negative.

19) Suppose we conduct an ANOVA test of four treatment means and reject the null hypothesis. Construction of a confidence interval for the difference between the first and second sample mean revealed the interval to be 10 plus or minus 12. We conclude

a. This pair of means differ.

b. This pair of means does not differ.

c. Because we do not know the units involved, we cannot draw any conclusion.

d. Because we do not know the degrees of freedom, we cannot draw any conclusion.

20) In a two-way ANOVA the second source of variation is due to

a. Random error.

b. Blocks.

c. Total variation

d. None of the above

21) A scatter diagram is a chart

a. In which the dependent variable is scaled along the vertical axis.

b. In which the independent variable is scaled along the horizontal axis.

c. That portrays the relationship between two variables.

d. All of the above.

22) In correlation analysis

a. We consider several independent variables.

b. We study the strength of the association between two variables.

c. We consider the intercept with the Y-axis.

d. None of the above.

23) The sample coefficient of correlation

a. Has the same sign as the slope, i.e. b.

b. Can range from -1.00 up to 1.00

c. Is also called Pearson=s r.

d. All of the above.

24) The coefficient of determination

a. Is the square of the coefficient of correlation.

b. Cannot be negative.

c. Reports the percent of the variation in the dependent variable explained by the independent variable.

d. All of the above.

25) Suppose we developed the following least squares regression equation: Y= = 3.5 + 2.1X. Which of the following statements are correct?

a. The dependent variable increases 2.1 for an increase of 1 in X.

b. The equation crosses the Y-axis at 3.5.

c. If X = 5, then Y= = 14.

d. All of the above.

26) The standard error of estimate is

a. Based on squared deviations from the regression line.

b. May assume negative values.

c. Is in squared units of the independent variable.

d. All of the above.

27) Which of the following is not a necessary condition for regression analysis.

a. The standard deviation of each of the conditional distributions must be the same.

b. The Y values are independent.

c. For each X value, there is a group of Y values and these Y values are normally distributed.

d. The slope of the regression line is positive (increasing).

28) Which of the following is not based on squared deviations from the regression line?

a. The coefficient of correlation.

b. The coefficient of determination.

c. The standard deviation.

d. The standard error of estimate.

29) In an ANOVA table for regression, the degrees of freedom for regression is

a. Equal to 1.

b. n - 1.

c. n - 2.

d. None of the above.

30) The term SSR/SS total is also called the

a. Sum of squares due to regression.

b. Coefficient of determination.

c. Standard error of estimate.

d. Coefficient of correlation.

**PART 5**

1) In a multiple regression equation there

a. Are two or more independent variables.

b. Is only one dependent variable.

c. Is one intercept value.

d. All of the above.

2) A dummy variable or indicator variable

a. May assume only a value of 0 or 1.

b. Is another term for the dependent variable.

c. Is found by (Y - Ŷ).

d. Is equal to Ŷ

3) The multiple standard error of estimate is

a. Is based on the (Y – Y)2.

b. Is negative when one of the net regression coefficients is 0.

c. Is found by taking the square root of SSR/SS total.

d. All of the above.

4) In the ANOVA table the value of k is

a. The number of independent variables.

b. The total number of observations

c. The number of degrees of freedom.

d. The sum of squares total.

5) A correlation matrix

a. Shows all simple coefficients of correlation.

b. Shows all possible net regression coefficients.

c. Shows the correlations that are positive.

d. Reports the multiple regression equation.

6) In a multiple regression equation

a. There is only one dependent variable.

b. The R2 term must be at least .50.

c. All the regression coefficient must be between -1.00 and 1.00.

d. None of the above.

7) Multicollinearity occurs when

a. The residuals are correlated.

b. Time is involved in the analysis

c. The independent variables are correlated.

d. The residuals are not constant for all Y' values.

8) In a global test of hypothesis we determine

a. Which independent variables do not equal 0.

b. Whether any of the set of independent variables differ from 0.

c. Whether any of the correlation coefficients differ from 0.

d. None of the above.

9) In testing the significance of individual regression coefficients

a. The test statistic is the t distribution.

b. We test the independent variables individually.

c. We usually delete the variables where the null hypothesis is not rejected.

d. All of the above.

10) The residual

a. Is the difference between the actual and the predicted value of the dependent variable.

b. Cannot assume a negative value.

c. Is also called the correlation matrix.

d. Has the same degrees of freedom as the MSE term.

11) To conduct a nonparametric test the

a. Population must follow the normal distribution.

b. The standard deviation must be known.

c. It is not necessary to make any assumption about the shape of the population.

d. The data must be at least interval scale.

12) Which of the following is not a characteristic of the X2

a. Its shape is based on the sample size.

b. It is not negative.

c. It is positively skewed.

d. It approaches a normal distribution as the degrees of freedom increase.

13) In a goodness-of-fit test where the sample size is 200, there are 5 categories, and the significance level is .05. The critical value of X2 is

a. 9.488

b. 11.070

c. 43.773

d. None of the above.

14) In a goodness-of-fit test

a. All the cell frequencies must be the same.

b. There must be at least 30 observations.

c. Forty percent of the cells must contain at least 10 observations.

d. None of the above.

15) In a contingency table

a. The number of rows must be the same as the number of columns.

b. A variable is classified according to two criteria.

c. There must be at least 10 observations in each cell.

d. All of the above.

16) In a contingency table a sample of 400 people is classified by gender and hair color (4 groups: blond, brown, black, and red). How many degrees of freedom are there?

a. 3

b. 8

c. 399

d. None of the above.

17) For a X2 goodness-of-fit test

a. There is only one degree of freedom.

b. The rejection region is in the upper right tail.

c. The scale of measurement is interval.

d. We must assume a normal population.

18) To find the expected frequency in a contingency table

a. Take the square root of the degrees of freedom.

b. Multiple the row total by the column total and divide the result by the grand total.

c. Use the total number of observations minus one.

d. None of these.

19) Suppose we select a sample of 100 observations and organize them into 6 categories. We wish to investigate whether the number of observations could be the same in each of the categories in the population. How many degrees of freedom are there?

a. 5

b. 97

c. 3

d. None of these.

20) Under what conditions could the X2 distribution assume negative values?

a. When the sample size is small.

b. When the cell frequencies are all equal.

c. When the degrees of freedom is 1.

d. Never

21) The philosophy of statistical quality control is to

a. Inspect the quality into the product.

b. Make it correct the first time.

c. Develop an adversarial relationship with the production department.

d. Shift costs from the manufacturing to the inspection department.

22) Dr. W. Edwards Deming

a. Was the founder of control charts.

b. Was an early craftsman in American industry.

c. Developed the ideas of acceptance sampling.

d. Helped Japan develop an overall plan to retool their production after World War II.

23) Chance variation is

a. Random in nature.

b. Can be completely eliminated from the process.

c. Is usually the result of a faulty production setup.

d. Is the basis of the Deming philosophy.

24) A Pareto Chart

a. Was developed by Dr. Walter A. Shewhart of the Bell Laboratories in the 1920s.

b. Is designed to show that 80 percent of the activity is caused by 20 percent of the factors.

c. Is one of Deming?s 14 points.

d. Highlights chance variation.

25) Which of the following is an example of a variable control chart?

a. An X- bar chart for means.

b. A percent defective chart.

c. A c- bar chart.

d. All of the above.

26) The Kimble Glass Company developed a control chart for the outside diameter of a syringe. Beginning at 7 AM this morning hourly checks showed the mean outside to diameter to be within the chart limits. Suddenly, the 2 PM check was above the UCL.

a. This is likely a random occurrence and production should be maintained.

b. This indicates that production is out of control. An adjustment should be made immediately.

c. This means that an error has been made in the calculation of the control limits.

d. This is an example of one of Deming?s 14 points.

27) The A2 factor is

a. Based on a constant relationship between the range and the standard deviation.

b. Used for variable charts.

c. Based on the size of the sample.

d. All of the above.

28) A c-bar chart shows the

a. Change in the mean.

b. Change in the range.

c. Number of defects per unit.

d. Percent defective.

29) The percent defective chart is

a. An example of a variable control chart.

b. A chart that shows the number of defects per unit.

c. A chart that shows the variation in weight of the unit produced.

d. An example of an attribute control chart.

30) In acceptance sampling the c value indicates the

a. Number of units sampled.

b. Probability of acceptance.

c. Number of defects per unit.

d. Allowable number of defects.

TRUE/FALSE: Mark the answers by circling T if the statement is true or F if the statement is false.

T F Q1: The number of individuals in a family is a continuous variable.

T F Q2: T-distributions are spread out more than a normal distribution with MU = 0, SIGMA = 1.

T F Q3: A random sample of 64 cars passing a check point on a certain highway showed a mean speed of 60 mph. The standard deviation of speeds is known to be 15 mph. In this case 60 mph is a point estimate of the population mean speed on this highway.

T F Q4: According to the Central Limit Theorem, the shape of the sampling distribution of sample mean (given that n ≥ 30) will be normal, whether or not the shape of the population is normal.

T F Q5: If the sample size is large (n ≥ 30), the standard deviation of the sample mean will equal the population standard deviation for that random variable.

T F Q6: Level of confidence is another name for level of significance.

T F Q7: If we would reject a null hypothesis at the 5% level, we would also reject it at the 1% level.

T F Q8: A Type I error is committed when one accepts the null hypothesis when it is false.

T F Q9: In a one-way ANOVA, when the null hypothesis is false, the calculated F-ratio would exceed the critical value of F for the chosen significance level.

T F Q10: Rejection of a hypothesis using a nonparametric test is more convincing than using an equivalent parametric test when the data are badly skewed.

T F Q11: Most nonparametric tests assume ordinal data.

T F Q12: One of the assumptions of regression analysis is that the error terms are normally distributed.

MULTIPLE CHOICE: Select the correct answer in each of Questions 11 to 25. There is only one correct answer to each question.

Q13: What area under the standard normal curve falls outside the Z values -1.96 and 1.96?

a. 0.05

b. 0.01

c. 0.90

d. 0.10

Q14: If each of a set of raw scores is transformed into a Z-score, the new distribution will have a standard deviation equal to

a. zero.

b. one.

c. the mean of the original distribution.

d. the standard deviation of the original distribution.

Q15: Which of the following random variables are continuous and which are discrete?

1. Score in a IQ Test

2. number of kittens in a litter

3. number of cars crossing a Traffic Light in one hour

4. the number of rainy days in a month

a. 1, 2 continuous; 3, 4 discrete

b. 1, 3, 4 continuous; 2 discrete

c. 4 continuous; 1, 2, 3 discrete

d. 1 continuous; 2, 3, 4 discrete

Q16: A factor that is varied by an experimenter in order to assess its effect is known as a(n):

a. dependent variable

b. independent variable

c. control variable

d. none of the above

Q17: For students' distribution, 90 percent of the area lies between t = -1.895 and t = 1.895 if the degrees of freedom are:

a. 6

b. 3

c. 7

d. 8

Q18: When (for what level of confidence) do we use Z = 1.645, for a two-sided test or confidence interval?

a. 90%

b. 95%

c. 80%

d. 100%

Q19: In finding confidence intervals for the mean of a normal population by using a t-statistic, student A uses a confidence coefficient of 0.95 while student B uses 0.99. Which one of the following statements is true about the length of the confidence intervals found by A and B?

a. B's interval will always be smaller than A's interval

b. B's interval will usually be smaller than A's interval

c. B's interval will always be larger than A's interval

d. B's interval will usually be larger than A's interval

Q20: We know the mean MU of a population. Suppose 1,000 samples of size n are drawn from this population. For each sample we compute a 90% confidence interval for MU. We would expect the mean of the population would NOT be contained within approximately how many of these intervals?

a. 0

b. 10

c. 100

d. 900

Q21: If the P-value for your test statistic satisfies p > .25, then:

a. you would not reject H(O) for ALPHA = .05

b. you would reject H(O) for ALPHA = .05

c. you would reject H(O) for ALPHA = .10

d. you would reject H(O) for ALPHA = .01

Q22:The appropriate alternative hypothesis for a lower tail test to determine if mean body weight of all the men who have joined a health club is less than 185 pounds would be

a. HA: μ ≥ 185 lb.

b. HA: μ < 185 lb.

c. HA: μ = 185 lb.

d. HA: μ ≠ 185 lb.

Q23: The e-mail usage for two different plants of a large company was compared at level of significance 0.05. A sample of 100 employees was selected at each plant. The mean number of e-mail messages sent per employee for one plant was 16 per week and the standard deviation was 4. For the other plant, the mean was 15 and the standard deviation was 3. For the test of equal population means versus unequal population means, the absolute value for the computed test statistic, the critical values, and the p-value respectively are:

a. 2, ± 1.96, 0.0455

b. 3, ± 2.33, 0.0027

c. 3, ± 1.96, 0.0455

d. 2, ± 1.65, 0.0455

Q24: Three samples of 10 were used to compare 3 population means. If the Sum of Squares Treatment (SST) is 350, what is the value for the Mean Square Treatment (MST)?

a. 350

b. 175

c. 35

d. 13

Q25: Which nonparametric test is analogous to a parametric two-sample t-test for means?

a. Wald-Wolfowitz test

b. Wilcoxon signed rank test

c. Mann-Whitney test

d. Kruskal-Wallis test

Q26: Which nonparametric test is analogous to a parametric t-test for differences in paired data?

a. Wald-Wolfowitz test

b. Wilcoxon signed rank test

c. Mann-Whitney test

d. Kruskal-Wallis test

Q27: Which nonparametric test is analogous to a one-factor ANOVA?

a. Wald-Wolfowitz test

b. Wilcoxon signed rank test

c. Mann-Whitney test

d. Kruskal-Wallis test

Q28: A linear regression between Y and X produced the following equation for the least squares line:

= -4.3 + 2.1x

Which of the following statements concerning this relationship is true?

a. For every one-unit increase in X, Y increases 4.3 units.

b. For every one-unit increase in X, Y decreases 2.1 units.

c. For every one-unit increase in X, Y decreases 4.3 units.

d. For every one-unit increase in X, Y increases 2.1 units.

Q29: The difference between an observed value of the dependent variable and its predicted value obtained from the regression equation is called a(n)

a. extrapolation.

b. interpolation.

c. residual.

d. mean deviation.

Q30: A regression line has been found and the statistician wants to know if the line has a slope. What is the appropriate null hypothesis to test?

a. H0: β1 = 0.

b. H0: β1 > 0.

c. H0: β1 < 0.

d. H0: β1 ≠ 0.

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