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Homework answers / question archive / 1)Hypotheses are tentative explanations of a principle operating in nature
1)Hypotheses are tentative explanations of a principle operating in nature.
2. The first step in testing a hypothesis is to establish a true null hypothesis and a false alternative hypothesis.
3. In testing hypotheses, the researcher initially assumes that the alternative hypothesis is true and uses the sample data to reject it.
4. The null and the alternative hypotheses must be mutually exclusive and collectively exhaustive.
5. Generally speaking, the hypotheses that business researchers want to prove are stated in the alternative hypothesis.
6. The probability of committing a Type I error is called the power of the test.
7. When a true null hypothesis is rejected, the researcher has made a Type I error.
8. When a false null hypothesis is rejected, the researcher has made a Type II error.
9. When a researcher fails to reject a false null hypothesis, a Type II error has been committed.
10. Power is equal to (1 –b), the probability of a test rejecting the null hypothesis that is indeed false.
11. The rejection region for a hypothesis test becomes smaller if the level of significance is changed from 0.01 to 0.05.
12. Whenever hypotheses are established such that the alternative hypothesis is ">", then this would be a two-tailed test
13. Whenever hypotheses are established such that the alternative hypothesis is "not equal to," the hypothesis test would be a two-tailed test.
14. If the researcher computes the probability of the calculated statistic and compares it to alpha, the level of significance to reach a decision, the researcher is using the p-value method for testing the hypotheses.
15. If a null hypothesis was not rejected at the 0.10 level of significance, it will be rejected at a 0.05 level of significance based on the same sample results.
16. The rejection and nonrejection regions are divided by a point called the critical value.
Multiple Choice
17. Consider the following null and alternative hypotheses.
Ho: m £ 67
Ha: m > 67
These hypotheses _______________.
a) indicate a one-tailed test with a rejection area in the right tail
b) indicate a one-tailed test with a rejection area in the left tail
c) indicate a two-tailed test
d) are established incorrectly
e) are not mutually exclusive
18. Consider the following null and alternative hypotheses.
Ho: m ³ 67
Ha: m < 67
These hypotheses _______________.
a) indicate a one-tailed test with a rejection area in the right tail
b) indicate a one-tailed test with a rejection area in the left tail
c) indicate a two-tailed test
d) are established incorrectly
e) are not mutually exclusive
19. Consider the following null and alternative hypotheses.
Ho: m = 67
Ha: m ¹ 67
These hypotheses ______________.
a) indicate a one-tailed test with a rejection area in the right tail
b) indicate a one-tailed test with a rejection area in the left tail
c) indicate a two-tailed test
d) are established incorrectly
e) are not mutually exclusive
20. Consider the following null and alternative hypotheses.
Ho: p £ 0.16
Ha: p > 0.16
These hypotheses _______________.
a) indicate a one-tailed test with a rejection area in the right tail
b) indicate a one-tailed test with a rejection area in the left tail
c) indicate a two-tailed test
d) are established incorrectly
e) are not mutually exclusive
21. Consider the following null and alternative hypotheses.
Ho: p ³ 0.16
Ha: p < 0.16
These hypotheses _______________.
a) indicate a one-tailed test with a rejection area in the right tail
b) indicate a one-tailed test with a rejection area in the left tail
c) indicate a two-tailed test
d) are established incorrectly
e) are not mutually exclusive
22. Consider the following null and alternative hypotheses.
Ho: p = 0.16
Ha: p ¹ 0.16
These hypotheses _______________.
a) indicate a one-tailed test with a rejection area in the right tail
b) indicate a one-tailed test with a rejection area in the left tail
c) indicate a two-tailed test
d) are established incorrectly
e) are not mutually exclusive
23. Suppose the alternative hypothesis in a hypothesis test is: "the population mean is less than 60". If the sample size is 50 and alpha =.05, the critical value of z is _______.
a) 1.645
b) -1.645
c) 1.96
d) -1.96
e) 2.05
24. Suppose the alternative hypothesis in a hypothesis test is "the population mean is greater than 60". If the sample size is 80 and alpha = .01, the critical value of z is _______.
a) 2.575
b) -2.575
c) 2.33
d) -2.33
e) 2.45
25. In a two-tailed hypothesis about a population mean with a sample size of 100 and alpha = 0.10, the rejection region would be _______.
a) z > 1.64
b) z > 1.28
c) z < -1.28 and z > 1.28
d) z < -1.64 and z > 1.64
e) z < -2.33 and z > 2.33
26. In a two-tailed hypothesis about a population mean with a sample size of 100 and α = 0.05, the rejection region would be _______.
a) z > 1.64
b) z > 1.96
c) z < -1.96 and z > 1.96
d) z < -1.64 and z > 1.64
e) z < -2.33 and z > 2.33
27. Suppose you are testing the null hypothesis that a population mean is less than or equal to 80, against the alternative hypothesis that the population mean is greater than 80. If the sample size is 49 and alpha = .10, the critical value of z is _______.
a) 1.645
b) -1.645
c) 1.28
d) -1.28
e) 2.33
28. Suppose you are testing the null hypothesis that a population mean is less than or equal to 80, against the alternative hypothesis that the population mean is greater than 80. The sample size is 49 and alpha =.05. If the sample mean is 84 and the population standard deviation is 14, the observed z value is _______.
a) 2
b) -2
c) 14
d) -14
e) 49
29. Suppose you are testing the null hypothesis that a population mean is greater than or equal to 60, against the alternative hypothesis that the population mean is less than 60. The sample size is 64 and a = .05. If the sample mean is 58 and the population standard deviation is 16, the observed z value is _______.
a) -1
b) 1
c) -8
d) 8
e) 58
30. A researcher is testing a hypothesis of a single mean. The critical z value for
a = .05 and an one?tailed test is 1.645. The observed z value from sample data is 1.13. The decision made by the researcher based on this information is to ______ the null hypothesis.
a) reject
b) not reject
c) redefine
d) change the alternate hypothesis into
e) restate the null hypothesis
31. A researcher is testing a hypothesis of a single mean. The critical z value for
a = .05 and a two?tailed test is +1.96. The observed z value from sample data is ?1.85. The decision made by the researcher based on this information is to _____ the null hypothesis.
a) reject
b) not reject
c) redefine
d) change the alternate hypothesis into
e) restate the null hypothesis
32. A researcher is testing a hypothesis of a single mean. The critical z value for
a = .05 and a two?tailed test is +1.96. The observed z value from sample data is 2.85. The decision made by the researcher based on this information is to _____ the null hypothesis.
a) reject
b) not reject
c) redefine
d) change the alternate hypothesis into
e) restate the null hypothesis
33. A researcher is testing a hypothesis of a single mean. The critical z value for a = .05 and a two?tailed test is +1.96. The observed z value from sample data is -2.11. The decision made by the researcher based on this information is to _____ the null hypothesis.
a) reject
b) not reject
c) redefine
d) change the alternate hypothesis into
e) restate the null hypothesis
34. A company produces an item that is supposed to have a six inch hole punched in the center. A quality control inspector is concerned that the machine which punches the hole is "out?of?control" (hole is too large or too small). In an effort to test this, the inspector is going to gather a sample punched by the machine and measure the diameter of the hole. The alternative hypothesis used to statistical test to determine if the machine is out?of?control is
a) the mean diameter is > 6 inches
b) the mean diameter is < 6 inches
c) the mean diameter is = 6 inches
d) the mean diameter is ≠ 6 inches
e) the mean diameter is ≥ 6 inches
35. Jennifer Cantu, VP of Customer Services at Tri-State Auto Insurance, Inc., monitors the claims processing time of the claims division. Her standard includes "a mean processing time of 5 days or less." Each week, her staff checks for compliance by analyzing a random sample of 60 claims. Jennifer's null hypothesis is ________.
a) m > 5
b) s > 5
c) n = 60
d) m < 5
e) m = 5
36. In performing a hypothesis test where the null hypothesis is that the population mean is 23 against the alternative hypothesis that the population mean is not equal to 23, a random sample of 17 items is selected. The sample mean is 24.6 and the sample standard deviation is 3.3. It can be assumed that the population is normally distributed. The degrees of freedom associated with this are _______.
a) 17
b) 16
c) 15
d) 2
e) 1
37. In performing a hypothesis test where the null hypothesis is that the population mean is 4.8 against the alternative hypothesis that the population mean is not equal to 4.8, a random sample of 25 items is selected. The sample mean is 4.1 and the sample standard deviation is 1.4. It can be assumed that the population is normally distributed. The degrees of freedom associated with this are _______.
a) 25
b) 24
c) 26
d) 2
e) 1
38. In performing a hypothesis test where the null hypothesis is that the population mean is 4.8 against the alternative hypothesis that the population mean is not equal to 4.8, a random sample of 25 items is selected. The sample mean is 4.1 and the sample standard deviation is 1.4. It can be assumed that the population is normally distributed. The level of significance is selected to be 0.10. The table "t" value for this problem is _______.
a) 1.318
b) 1.711
c) 2.492
d) 2.797
e) 3.227
39. In performing a hypothesis test where the null hypothesis is that the population mean is 4.8 against the alternative hypothesis that the population mean is not equal to 4.8, a random sample of 25 items is selected. The sample mean is 4.1 and the sample standard deviation is 1.4. It can be assumed that the population is normally distributed. The observed "t" value for this problem is _______.
a) -12.5
b) 12.5
c) -2.5
d) -0.7
e) 0.7
40. In performing a hypothesis test where the null hypothesis is that the population mean is 6.9 against the alternative hypothesis that the population mean is not equal to 6.9, a random sample of 16 items is selected. The sample mean is 7.1 and the sample standard deviation is 2.4. It can be assumed that the population is normally distributed. The observed "t" value for this problem is _______.
a) 0.05
b) 0.20
c) 0.33
d) 1.33
e) 1.43
41. In performing a hypothesis test where the null hypothesis is that the population mean is 6.9 against the alternative hypothesis that the population mean is not equal to 6.9, a random sample of 16 items is selected. The sample mean is 7.1 and the sample standard deviation is 2.4. It can be assumed that the population is normally distributed. The level of significance is selected as 0.05. The table "t" value for this problem is _______.
a) 1.753
b) 2.947
c) 2.120
d) 2.131
e) 2.311
42. In performing a hypothesis test where the null hypothesis is that the population mean is 6.9 against the alternative hypothesis that the population mean is not equal to 6.9, a random sample of 16 items is selected. The sample mean is 7.1 and the sample standard deviation is 2.4. It can be assumed that the population is normally distributed. The level of significance is selected as 0.05. The decision rule for this problem is to reject the null hypothesis if the observed "t" value is _______.
a) less than -2.131 or greater than 2.131
b) less than -1.761 or greater than 1.761
c) less than -1.753 or greater than 1.753
d) less than -2.120 or greater than 2.120
e) less than -3.120 or greater than 3.120
43. The diameter of 3.5 inch diskettes is normally distributed. Periodically, quality control inspectors at Dallas Diskettes randomly select a sample of 16 diskettes. If the mean diameter of the diskettes is too large or too small the diskette punch is shut down for adjustment; otherwise, the punching process continues. The last sample showed a mean and standard deviation of 3.49 and 0.08 inches, respectively. Using a = 0.05, the critical "t" values are _______.
a) -2.120 and 2.120
b) -2.131 and 2.131
c) -1.753 and 1.753
d) -1.746 and 1.746
e) -2.567 and 2.567
44. The diameter of 3.5 inch diskettes is normally distributed. Periodically, quality control inspectors at Dallas Diskettes randomly select a sample of 16 diskettes. If the mean diameter of the diskettes is too large or too small the diskette punch is shut down for adjustment; otherwise, the punching process continues. The null hypothesis is ______.
a) n ¹ 16
b) n = 16
c) m = 3.5
d) m ¹ 3.5
e) m ≥ 3.5
45. The diameter of 3.5 inch diskettes is normally distributed. Periodically, quality control inspectors at Dallas Diskettes randomly select a sample of 16 diskettes. If the mean diameter of the diskettes is too large or too small the diskette punch is shut down for adjustment; otherwise, the punching process continues. The last sample showed a mean and standard deviation of 3.49 and 0.08 inches, respectively. Using a = 0.05, the appropriate decision is _______.
a) reject the null hypothesis and shut down the punch
b) reject the null hypothesis and do not shut down the punch
c) do not reject the null hypothesis and shut down the punch
d) do not reject the null hypothesis and do shut down the punch
e) do nothing
46. The diameter of 3.5 inch diskettes is normally distributed. Periodically, quality control inspectors at Dallas Diskettes randomly select a sample of 16 diskettes. If the mean diameter of the diskettes is too large or too small the diskette punch is shut down for adjustment; otherwise, the punching process continues. The last sample showed a mean and standard deviation of 3.55 and 0.08 inches, respectively. Using a = 0.05, the appropriate decision is _______.
a) reject the null hypothesis and shut down the punch
b) reject the null hypothesis and do not shut down the punch
c) do not reject the null hypothesis and shut down the punch
d) do not reject the null hypothesis and do not shut down the punch
e) do nothing
47. In performing hypothesis tests about the population mean, the population standard deviation should be used if it is known. If it is not known, which of the following statistical test should be used?
a) z test of a population mean
b) t test of a population mean
c) z test of a population proportion
d) c2 test of a population variance
e) t test of a population proportion
48. In performing hypothesis tests about the population mean, the population standard deviation should be used if it is known. If it is not known, a t test can be used to test the mean if _________________.
a) the sample size is at least thirty
b) the sample is random
c) the population mean is known
d) the population is normally distributed
e) the population is chi-square distributed
49. Suppose a researcher is testing a null hypothesis that m = 61. A random sample of n = 36 is taken resulting in a sample mean of 63 and s = 9. The observed t value is _______.
a) -0.22
b) 0.22
c) 1.33
d) 8.08
e) 7.58
50. A political scientist wants to prove that a candidate is currently carrying more than 60% of the vote in the state. She has her assistants randomly sample 200 eligible voters in the state by telephone and only 90 declare that they support her candidate. The observed z value for this problem is _______.
a) -4.33
b) 4.33
c) 0.45
d) -.31
e) 2.33
51. A company believes that it controls more than 30% of the total market share for one of its products. To prove this belief, a random sample of 144 purchases of this product is contacted. It is found that 50 of the 144 purchased this company's brand of the product. If a researcher wants to conduct a statistical test for this problem, the alternative hypothesis would be _______.
a) the population proportion is less than 0.30
b) the population proportion is greater than 0.30
c) the population proportion is not equal to 0.30
d) the population mean is less than 40
e) the population mean is greater than 40
52. A company believes that it controls more than 30% of the total market share for one of its products. To prove this belief, a random sample of 144 purchases of this product is contacted. It is found that 50 of the 144 purchased this company's brand of the product. If a researcher wants to conduct a statistical test for this problem, the observed z value would be _______.
a) 0.05
b) 0.103
c) 0.35
d) 1.24
e) 1.67
53. A company believes that it controls more than 30% of the total market share for one of its products. To prove this belief, a random sample of 144 purchases of this product is contacted. It is found that 50 of the 144 purchased this company's brand of the product. If a researcher wants to conduct a statistical test for this problem, the test would be _______.
a) a one-tailed test
b) a two-tailed test
c) an alpha test
d) a finite population test
e) a finite sample test
54. Ophelia O'Brien, VP of Consumer Credit of American First Banks (AFB), monitors the default rate on personal loans at the AFB member banks. One of her standards is "no more than 5% of personal loans should be in default." On each Friday, the default rate is calculated for a sample of 500 personal loans. Last Friday's sample contained 30 defaulted loans. Ophelia's null hypothesis is _______.
a) p > 0.05
b) p = 0.05
c) n = 30
d) n = 500
e) n = 0.05
55. Ophelia O'Brien, VP of Consumer Credit of American First Banks (AFB), monitors the default rate on personal loans at the AFB member banks. One of her standards is "no more than 5% of personal loans should be in default." On each Friday, the default rate is calculated for a sample of 500 personal loans. Last Friday's sample contained 30 defaulted loans. Using a = 0.10, the critical z value is _______.
a) 1.645
b) -1.645
c) 1.28
d) -1.28
e) 2.28
56. Ophelia O'Brien, VP of Consumer Credit of American First Banks (AFB), monitors the default rate on personal loans at the AFB member banks. One of her standards is "no more than 5% of personal loans should be in default." On each Friday, the default rate is calculated for a sample of 500 personal loans. Last Friday's sample contained 30 defaulted loans. Using a = 0.10, the observed z value is _______.
a) 1.03
b) -1.03
c) 0.046
d) -0.046
e) 1.33
57. Ophelia O'Brien, VP of Consumer Credit of American First Banks (AFB), monitors the default rate on personal loans at the AFB member banks. One of her standards is "no more than 5% of personal loans should be in default." On each Friday, the default rate is calculated for a sample of 500 personal loans. Last Friday's sample contained 30 defaulted loans. Using a = 0.10, the appropriate decision is _______.
a) reduce the sample size
b) increase the sample size
c) reject the null hypothesis
d) do not reject the null hypothesis
e) do nothing
58. Ophelia O'Brien, VP of Consumer Credit of American First Banks (AFB), monitors the default rate on personal loans at the AFB member banks. One of her standards is "no more than 5% of personal loans should be in default." On each Friday, the default rate is calculated for a sample of 500 personal loans. Last Friday's sample contained 38 defaulted loans. Using a = 0.10, the appropriate decision is _______.
a) reduce the sample size
b) increase the sample size
c) reject the null hypothesis
d) do not reject the null hypothesis
e) do nothing
59. The executives of CareFree Insurance, Inc. feel that "a majority of our employees perceive a participatory management style at CareFree." A random sample of 200 CareFree employees is selected to test this hypothesis at the 0.05 level of significance. Eighty employees rate the management as participatory. The null hypothesis is __________.
a) n = 30
b) n = 200
c) p = 0.50
d) p < 0.50
e) n > 200
60. The executives of CareFree Insurance, Inc. feel that "a majority of our employees perceive a participatory management style at CareFree." A random sample of 200 CareFree employees is selected to test this hypothesis at the 0.05 level of significance. Eighty employees rate the management as participatory. The appropriate decision is __________.
a) do not reject the null hypothesis
b) reject the null hypothesis
c) reduce the sample size
d) increase the sample size
e) do nothing
61. The executives of CareFree Insurance, Inc. feel that "a majority of our employees perceive a participatory management style at CareFree." A random sample of 200 CareFree employees is selected to test this hypothesis at the 0.05 level of significance. Ninety employees rate the management as participatory. The appropriate decision is __________.
a) do not reject the null hypothesis
b) reject the null hypothesis
c) reduce the sample size
d) increase the sample size
e) maintain status quo
62. Elwin Osbourne, CIO at GFS, Inc., suspects that at least 25% of e-mail messages sent by GFS employees are not business related. A random sample of 300 e-mail messages was selected to test this hypothesis at the 0.01 level of significance. Fifty-four of the messages were not business related. The null hypothesis is ____.
a) b = 30
b) n = 300
c) p < 0.25
d) p ≠ 0.25
e) p = 0.25
63. Elwin Osbourne, CIO at GFS, Inc., suspects that at least 25% of e-mail messages sent by GFS employees are not business related. A random sample of 300 e-mail messages was selected to test this hypothesis at the 0.01 level of significance. Fifty-four of the messages were not business related. The appropriate decision is _______.
a) increase the sample size
b) gather more data
c) reject the null hypothesis
d) do not reject the null hypothesis
e) maintain status quo
64. Elwin Osbourne, CIO at GFS, Inc., suspects that at least 25% of e-mail messages sent by GFS employees are not business related. A random sample of 300 e-mail messages was selected to test this hypothesis at the 0.01 level of significance. Sixty of the messages were not business related. The appropriate decision is _______.
a) increase the sample size
b) gather more data
c) maintain status quo
d) do not reject the null hypothesis
e) reject the null hypothesis
65. A null hypothesis is p > 0.65. To test this hypothesis, a sample of 400 is taken and alpha is set at 0.05. If the true proportion is p = 0.60, what is the probability of a type II error?
a) 0.17
b) 0.45
c) 0.95
d) 0.67
e) 0.33
66. Discrete Components, Inc. manufactures a line of electrical resistors. Presently, the carbon composition line is producing 100 ohm resistors. The population variance of these resistors "must not exceed 4" to conform to industry standards. Periodically, the quality control inspectors check for conformity by randomly select 10 resistors from the line, and calculating the sample variance. The last sample had a variance of 4.36. Assume that the population is normally distributed. Using a = 0.05, the null hypothesis is _________________.
a) m = 100
b) s £ 10
c) s2 ³ 4
d) s2 = 4
e) n = 100
67. Discrete Components, Inc. manufactures a line of electrical resistors. Presently, the carbon composition line is producing 100 ohm resistors. The population variance of these resistors "must not exceed 4" to conform to industry standards. Periodically, the quality control inspectors check for conformity by randomly select 10 resistors from the line, and calculating the sample variance. The last sample had a variance of 4.36. Assume that the population is normally distributed. Using a = 0.05, the critical value of chi-square is _________________.
a) 18.31
b) 16.92
c) 3.94
d) 3.33
e) 19.82
68. Discrete Components, Inc. manufactures a line of electrical resistors. Presently, the carbon composition line is producing 100 ohm resistors. The population variance of these resistors "must not exceed 4" to conform to industry standards. Periodically, the quality control inspectors check for conformity by randomly select 10 resistors from the line, and calculating the sample variance. The last sample had a variance of 4.36. Assume that the population is normally distributed. Using a = 0.05, the observed value of chi-square is _________________.
a) 1.74
b) 1.94
c) 10.90
d) 9.81
e) 8.91
69. Discrete Components, Inc. manufactures a line of electrical resistors. Presently, the carbon composition line is producing 100 ohm resistors. The population variance of these resistors "must not exceed 4" to conform to industry standards. Periodically, the quality control inspectors check for conformity by randomly select 10 resistors from the line, and calculating the sample variance. The last sample had a variance of 4.36. Assume that the population is normally distributed. Using a = 0.05, the appropriate decision is _________________.
a) increase the sample size
b) reduce the sample size
c) reject the null hypothesis
d) do not reject the null hypothesis
e) maintain status quo
70. David Desreumaux, VP of Human Resources of American First Banks (AFB), is reviewing the employee training programs of AFB banks. Based on a recent census of personnel, David knows that the variance of teller training time in the Southeast region is 8, and he wonders if the variance in the Southwest region is the same number. His staff randomly selected personnel files for 15 tellers in the Southwest Region, and determined that their mean training time was 25 hours and that the standard deviation was 4 hours. Assume that teller training time is normally distributed in the population. Using a = 0.10, the null hypothesis is ________.
a) m = 25
b) s2 = 8
c) s2 = 4
d) s2 £ 8
e) s2 = 16
71. David Desreumaux, VP of Human Resources of American First Banks (AFB), is reviewing the employee training programs of AFB banks. Based on a recent census of personnel, David knows that the variance of teller training time in the Southeast region is 8, and he wonders if the variance in the Southwest region is the same number. His staff randomly selected personnel files for 15 tellers in the Southwest Region, and determined that their mean training time was 25 hours and that the standard deviation was 4 hours. Assume that teller training time is normally distributed in the population. Using a = 0.10, the critical values of chi-square are ________.
a) 7.96 and 26.30
b) 6.57 and 23.68
c) -1.96 and 1.96
d) -1.645 and 1.645
e) -6.57 and 23.68
72. David Desreumaux, VP of Human Resources of American First Banks (AFB), is reviewing the employee training programs of AFB banks. Based on a recent census of personnel, David knows that the variance of teller training time in the Southeast region is 8, and he wonders if the variance in the Southwest region is the same number. His staff randomly selected personnel files for 15 tellers in the Southwest Region, and determined that their mean training time was 25 hours and that the standard deviation was 4 hours. Assume that teller training time is normally distributed in the population. Using a = 0.10, the observed value of chi-square is ________.
a) 28.00
b) 30.00
c) 56.00
d) 60.00
e) 65.00
73. David Desreumaux, VP of Human Resources of American First Banks (AFB), is reviewing the employee training programs of AFB banks. Based on a recent census of personnel, David knows that the variance of teller training time in the Southeast region is 8, and he wonders if the variance in the Southwest region is the same number. His staff randomly selected personnel files for 15 tellers in the Southwest Region, and determined that their mean training time was 25 hours and that the standard deviation was 4 hours. Assume that teller training time is normally distributed in the population. Using a = 0.10, the appropriate decision is ________.
a) increase the sample size
b) reduce the sample size
c) do not reject the null hypothesis
d) maintain status quo
e) reject the null hypothesis
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