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Homework answers / question archive / University of Tech - Iraq - QMDS 101 CHAPTER 9: FUNDAMENTALS OF HYPOTHESIS TESTING: ONE-SAMPLE TESTS 1)Which of the following would be an appropriate null hypothesis? The mean of a population is equal to 55

University of Tech - Iraq - QMDS 101 CHAPTER 9: FUNDAMENTALS OF HYPOTHESIS TESTING: ONE-SAMPLE TESTS 1)Which of the following would be an appropriate null hypothesis? The mean of a population is equal to 55

Statistics

University of Tech - Iraq - QMDS 101

CHAPTER 9: FUNDAMENTALS OF HYPOTHESIS TESTING: ONE-SAMPLE TESTS

1)Which of the following would be an appropriate null hypothesis?

    1. The mean of a population is equal to 55.
    2. The mean of a sample is equal to 55.
    3. The mean of a population is greater than 55.
    4. Only (a) and (c) are true.

 

 

 

  1. Which of the following would be an appropriate null hypothesis?
    1. The population proportion is less than 0.65.
    2. The sample proportion is less than 0.65.
    3. The population proportion is no less than 0.65.
    4. The sample proportion is no less than 0.65.

 

 

  1. Which of the following would be an appropriate alternative hypothesis?
    1. The mean of a population is equal to 55.
    2. The mean of a sample is equal to 55.
    3. The mean of a population is greater than 55.
    4. The mean of a sample is greater than 55.

 

  1. Which of the following would be an appropriate alternative hypothesis?
    1. The population proportion is less than 0.65.
    2. The sample proportion is less than 0.65.
    3. The population proportion is no less than 0.65.
    4. The sample proportion is no less than 0.65.

 

 

  1. A Type II error is committed when
    1. we reject a null hypothesis that is true.
    2. we don't reject a null hypothesis that is true.
    3. we reject a null hypothesis that is false.
    4. we don't reject a null hypothesis that is false.

 

 

  1. A Type I error is committed when
    1. we reject a null hypothesis that is true.
    2. we don't reject a null hypothesis that is true.
    3. we reject a null hypothesis that is false.
    4. we don't reject a null hypothesis that is false.

 

 

  1. The power of a test is measured by its capability of
    1. rejecting a null hypothesis that is true.
    2. not rejecting a null hypothesis that is true.
    3. rejecting a null hypothesis that is false.
    4. not rejecting a null hypothesis that is false.

 

 

  1. If we are performing a two-tailed test of whether = 100, the probability of detecting a shift of the mean to 105 will be ________ the probability of detecting a shift of the mean to 110.
    1. less than
    2. greater than
    3. equal to
    4. not comparable to

 

 

 

  1. True or False: For a given level of significance, if the sample size is increased, the power of the test will increase.

 

 

  1. True or False: For a given level of significance, if the sample size is increased, the probability of committing a Type I error will increase.

 

 

  1. True or False: For a given level of significance, if the sample size is increased, the probability of committing a Type II error will increase.

 

 

  1. True or False: For a given sample size, the probability of committing a Type II error will increase when the probability of committing a Type I error is reduced.

 

 

  1. If an economist wishes to determine whether there is evidence that average family income in a community exceeds $25,000
    1. either a one-tailed or two-tailed test could be used with equivalent results.
    2. a one-tailed test should be utilized.
    3. a two-tailed test should be utilized.
    4. None of the above.

 

 

  1. If an economist wishes to determine whether there is evidence that average family income in a community equals $25,000
    1. either a one-tailed or two-tailed test could be used with equivalent results.
    2. a one-tailed test should be utilized.
    3. a two-tailed test should be utilized.
    4. None of the above.

 

 

  1. If the p-value is less than  in a two-tailed test,
    1. the null hypothesis should not be rejected.
    2. the null hypothesis should be rejected.
    3. a one-tailed test should be used.
    4. no conclusion should be reached.

 

 

  1. If a test of hypothesis has a Type I error probability () of 0.01, we mean
    1. if the null hypothesis is true, we don't reject it 1% of the time.
    2. if the null hypothesis is true, we reject it 1% of the  time.
    3. if the null hypothesis is false, we don't reject it 1% of the time.
    4. if the null hypothesis is false, we reject it 1% of the time.

 

 

  1. If the Type I error () for a given test is to be decreased, then for a fixed sample size n
    1. the Type II error () will also decrease.
    2. the Type II error () will increase.
    3. the power of the test will increase.
    4. a one-tailed test must be utilized.

 

 

  1. For a given sample size n, if the level of significance () is decreased, the power of the test
    1. will increase.
    2. will decrease.
    3. will remain the same.
    4. cannot be determined.

 

 

  1. For a given level of significance (), if the sample size n is increased, the probability of a Type II error ()
    1. will decrease.
    2. will increase.
    3. will remain the same.
    4. cannot be determined.

 

 

  1. If a researcher rejects a true null hypothesis, she has made a _______error.

 

  1. If a researcher accepts a true null hypothesis, she has made a _______decision.

 

  1. If a researcher rejects a false null hypothesis, she has made a _______decision.

 

  1. If a researcher accepts a false null hypothesis, she has made a _______error.

 

  1. It is possible to directly compare the results of a confidence interval estimate to the results obtained by testing a null hypothesis if
    1. a two-tailed test for  is used.
    2. a one-tailed test for  is used.
    3. Both of the previous statements are true.
    4. None of the previous statements is true.

 

 

  1. The power of a statistical test is
    1. the probability of not rejecting H0 when it is false.
    2. the probability of rejecting H0 when it is true.
    3. the probability of not rejecting H0 when it is true.
    4. the probability of rejecting H0 when it is false.

 

 

  1. The symbol for the power of a statistical test is
    1. .
    2. 1 – .
    3. .
    4. 1 – .

 

 

  1. Suppose we wish to test H0:  47 versus H1:  > 47. What will result if we conclude that the mean is greater than 47 when its true value is really 52?
    1. We have made a Type I error.
    2. We have made a Type II error.
    3. We have made a correct decision
    4. None of the above are correct.

 

 

  1. How many Kleenex should the Kimberly Clark Corporation package of tissues contain? Researchers determined that 60 tissues is the average number of tissues used during a cold. Suppose a random sample of 100 Kleenex users yielded the following data on the number of tissues used during a cold:  = 52, s = 22. Give the null and alternative hypotheses to determine if the number of tissues used during a cold is less than 60.

 

 

  1. How many Kleenex should the Kimberly Clark Corporation package of tissues contain? Researchers determined that 60 tissues is the average number of tissues used during a cold. Suppose a random sample of 100 Kleenex users yielded the following data on the number of tissues used during a cold:  = 52, s = 22. Using the sample information provided, calculate the value of the test statistic.
    1.  

 

 

  1. How many Kleenex should the Kimberly Clark Corporation package of tissues contain? Researchers determined that 60 tissues is the average number of tissues used during a cold. Suppose a random sample of 100 Kleenex users yielded the following data on the number of tissues used during a cold:  = 52, s = 22. Suppose the alternative we wanted to test was . State the correct rejection region for  = 0.05.
    1. Reject H0 if t > 1.6604.
    2. Reject H0 if t < – 1.6604.
    3. Reject H0 if t > 1.9842 or Z < – 1.9842.
    4. Reject H0 if t < – 1.9842.

 

 

  1. How many Kleenex should the Kimberly Clark Corporation package of tissues contain? Researchers determined that 60 tissues is the average number of tissues used during a cold. Suppose a random sample of 100 Kleenex users yielded the following data on the number of tissues used during a cold:  = 52, s = 22. Suppose the test statistic does fall in the rejection region at  = 0.05. Which of the following decision is correct?
    1. At  = 0.05, we do not reject H0.
    2. At  = 0.05, we reject H0.
    3. At  = 0.05, we accept H0.
    4. At  = 0.10, we do not reject H0.

 

 

  1. How many Kleenex should the Kimberly Clark Corporation package of tissues contain? Researchers determined that 60 tissues is the average number of tissues used during a cold. Suppose a random sample of 100 Kleenex users yielded the following data on the number of tissues used during a cold:  = 52, s = 22. Suppose the test statistic does fall in the rejection region at  = 0.05. Which of the following conclusion is correct?
    1. At  = 0.05, there is not sufficient evidence to conclude that the average number of tissues used during a cold is 60 tissues.
    2. At  = 0.05, there is sufficient evidence to conclude that the average number of tissues used during a cold is 60 tissues.
    3. At  = 0.05, there is not sufficient evidence to conclude that the average number of tissues used during a cold is not 60 tissues.
    4. At  = 0.10, there is sufficient evidence to conclude that the average number of tissues used during a cold is not 60 tissues.

 

 

  1. We have created a 95% confidence interval for  with the result (10, 15). What decision will we make if we test  at  = 0.05?
    1. Reject H0 in favor of H1.
    2. Accept H0 in favor of H1.
    3. Fail to reject H0 in favor of H1.
    4. We cannot tell what our decision will be from the information given.

 

 

 

 

 

 

 

  1. We have created a 95% confidence interval for  with the result (10, 15). What decision will we make if we test  at  = 0.10?
    1. Reject H0 in favor of H1.
    2. Accept H0 in favor of H1.
    3. Fail to reject H0 in favor of H1.
    4. We cannot tell what our decision will be from the information given.

 

  1. We have created a 95% confidence interval for  with the result (10, 15). What decision will we make if we test  at  = 0.025?
    1. Reject H0 in favor of H1.
    2. Accept H0 in favor of H1.
    3. Fail to reject H0 in favor of H1.
    4. We cannot tell what our decision will be from the information given.

 

 

  1. Suppose we want to test . Which of the following possible sample results based on a sample of size 36 gives the strongest evidence to reject H0 in favor of H1?
    1.  = 28, s = 6
    2.  = 27, s = 4
    3.  = 32, s = 2
    4.  = 26, s = 9

 

 

  1. Which of the following statements is not true about the level of significance in a hypothesis test?
    1. The larger the level of significance, the more likely you are to reject the null hypothesis.
    2. The level of significance is the maximum risk we are willing to accept in making a Type I error.
    3. The significance level is also called the  level.
    4. The significance level is another name for Type II error.

 

 

  1. If, as a result of a hypothesis test, we reject the null hypothesis when it is false, then we have committed
    1. a Type II error.
    2. a Type I error.
    3. no error.
    4. an acceptance error.

 

 

  1. The value that separates a rejection region from a non-rejection region is called the _______.

 

  1. A                           is a numerical quantity computed from the data of a sample and is used in reaching a decision on whether or not to reject the null hypothesis.
    1. significance level
    2. critical value
    3. test statistic
    4. parameter

 

 

 

  1. The owner of a local nightclub has recently surveyed a random sample of n = 250 customers of the club. She would now like to determine whether or not the mean age of her customers is over 30. If so, she plans to alter the entertainment to appeal to an older crowd. If not, no entertainment changes will be made. The appropriate hypotheses to test are:
    1. .
    2. .
    3. .
    4. .

 

 

 

  1. The owner of a local nightclub has recently surveyed a random sample of n = 250 customers of the club. She would now like to determine whether or not the mean age of her customers is over 30. If so, she plans to alter the entertainment to appeal to an older crowd. If not, no entertainment changes will be made. If she wants to be 99% confident in her decision, what rejection region should she use?
    1. Reject H0 if t < – 2.34.
    2. Reject H0 if t < – 2.55.
    3. Reject H0 if t > 2.34.
    4. Reject H0 if t > 2.58.

 

 

 

  1. The owner of a local nightclub has recently surveyed a random sample of n = 250 customers of the club. She would now like to determine whether or not the mean age of her customers is over 30. If so, she plans to alter the entertainment to appeal to an older crowd. If not, no entertainment changes will be made. Suppose she found that the sample mean was 30.45 years and the sample standard deviation was 5 years. If she wants to be 99% confident in her decision, what decision should she make?
    1. Reject H0.
    2. Accept H0.
    3. Fail to reject H0.
    4. We cannot tell what her decision should be from the information given.

 

 

 

  1. The owner of a local nightclub has recently surveyed a random sample of n = 250 customers of the club. She would now like to determine whether or not the mean age of her customers is over 30. If so, she plans to alter the entertainment to appeal to an older crowd. If not, no entertainment changes will be made. Suppose she found that the sample mean was 30.45 years and the sample standard deviation was 5 years. If she wants to be 99% confident in her decision, what conclusion can she make?
    1. There is not sufficient evidence that the mean age of her customers is over 30.
    2. There is sufficient evidence that the mean age of her customers is over 30.
    3. There is not sufficient evidence that the mean age of her customers is not over 30.
    4. There is sufficient evidence that the mean age of her customers is not over 30.

 

 

 

  1. The owner of a local nightclub has recently surveyed a random sample of n = 250 customers of the club. She would now like to determine whether or not the mean age of her customers is over 30. If so, she plans to alter the entertainment to appeal to an older crowd. If not, no entertainment changes will be made. Suppose she found that the sample mean was 30.45 years and the sample standard deviation was 5 years. What is the p-value associated with the test statistic?
    1. 0.3577
    2. 0.1423
    3. 0.0780
    4. 0.02

 

 

 

  1. A survey claims that 9 out of 10 doctors recommend aspirin for their patients with headaches. To test this claim against the alternative that the actual proportion of doctors who recommend aspirin is less than 0.90, a random sample of 100 doctors results in 83 who indicate that they recommend aspirin. The value of the test statistic in this problem is approximately equal to:
    1. – 4.12
    2. – 2.33
    3. – 1.86
    4. – 0.07

 

 

 

  1. A survey claims that 9 out of 10 doctors recommend aspirin for their patients with headaches. To test this claim against the alternative that the actual proportion of doctors who recommend aspirin is less than 0.90, a random sample of 100 doctors was selected. Suppose that the test statistic is – 2.20. Can we conclude that H0 should be rejected at the (a)  = 0.10, (b)  = 0.05, and (c)  = 0.01 level of Type I error?
    1. (a) yes; (b) yes; (c) yes
    2. (a) no; (b) no; (c) no
    3. (a) no; (b) no; (c) yes
    4. (a) yes; (b) yes; (c) no

 

 

 

  1. A survey claims that 9 out of 10 doctors recommend aspirin for their patients with headaches. To test this claim against the alternative that the actual proportion of doctors who recommend aspirin is less than 0.90, a random sample of 100 doctors was selected. Suppose you reject the null hypothesis. What conclusion can you draw?
    1. There is not sufficient evidence that the proportion of doctors who recommend aspirin is not less than 0.90.
    2. There is sufficient evidence that the proportion of doctors who recommend aspirin is not less than 0.90.
    3. There is not sufficient evidence that the proportion of doctors who recommend aspirin is less than 0.90.
    4. There is sufficient evidence that the proportion of doctors who recommend aspirin is less than 0.90.

 

 

 

  1. A major videocassette rental chain is considering opening a new store in an area that currently does not have any such stores. The chain will open if there is evidence that more than 5,000 of the 20,000 households in the area are equipped with videocassette recorders (VCRs). It conducts a telephone poll of 300 randomly selected households in the area and finds that 96 have VCRs. State the test of interest to the rental chain.

 

 

 

  1. A major videocassette rental chain is considering opening a new store in an area that currently does not have any such stores. The chain will open if there is evidence that more than 5,000 of the 20,000 households in the area are equipped with videocassette recorders (VCRs). It conducts a telephone poll of 300 randomly selected households in the area and finds that 96 have VCRs. The value of the test statistic in this problem is approximately equal to:
    1. 2.80
    2. 2.60
    3. 1.94
    4. 1.30

 

 

 

  1. A major videocassette rental chain is considering opening a new store in an area that currently does not have any such stores. The chain will open if there is evidence that more than 5,000 of the 20,000 households in the area are equipped with videocassette recorders (VCRs). It conducts a telephone poll of 300 randomly selected households in the area and finds that 96 have VCRs. The p-value associated with the test statistic in this problem is approximately equal to:
    1. 0.0100
    2. 0.0051
    3. 0.0026
    4. 0.0013

 

 

 

  1. A major videocassette rental chain is considering opening a new store in an area that currently does not have any such stores. The chain will open if there is evidence that more than 5,000 of the 20,000 households in the area are equipped with videocassette recorders (VCRs). It conducts a telephone poll of 300 randomly selected households in the area and finds that 96 have VCRs. The decision on the hypothesis test using a 3% level of significance is:
    1. to reject H0 in favor of H1.
    2. to accept H0 in favor of H1.
    3. to fail to reject H0 in favor of H1.
    4. we cannot tell what the decision should be from the information given.

 

 

 

  1. A major videocassette rental chain is considering opening a new store in an area that currently does not have any such stores. The chain will open if there is evidence that more than 5,000 of the 20,000 households in the area are equipped with videocassette recorders (VCRs). It conducts a telephone poll of 300 randomly selected households in the area and finds that 96 have VCRs. The rental chain's conclusion from the hypothesis test using a 3% level of significance is:
    1. to open a new store.
    2. not to open a new store.
    3. to delay opening a new store until additional evidence is collected.
    4. we cannot tell what the decision should be from the information given.

 

 

 

  1. An entrepreneur is considering the purchase of a coin-operated laundry. The current owner claims that over the past 5 years, the average daily revenue was $675 with a standard deviation of $75. A sample of 30 days reveals a daily average revenue of $625. If you were to test the null hypothesis that the daily average revenue was $675, which test would you use?
    1. Z-test of a population mean
    2. Z-test of a population proportion
    3. t-test of  a population mean
    4. t-test of  a population proportion

 

 

 

  1. An entrepreneur is considering the purchase of a coin-operated laundry. The current owner claims that over the past 5 years, the average daily revenue was $675 with a standard deviation of $75. A sample of 30 days reveals a daily average revenue of $625. If you were to test the null hypothesis that the daily average revenue was $675 and decide not to reject the null hypothesis, what can you conclude?
    1. There is not enough evidence to conclude that the daily average revenue was $675.
    2. There is not enough evidence to conclude that the daily average revenue was not $675.
    3. There is enough evidence to conclude that the daily average revenue was $675.
    4. There is enough evidence to conclude that the daily average revenue was not $675.

 

 

 

  1. A manager of the credit department for an oil company would like to determine whether the average monthly balance of credit card holders is equal to $75. An auditor selects a random sample of 100 accounts and finds that the average owed is $83.40 with a sample standard deviation of $23.65. If you wanted to test whether the auditor should conclude that there is evidence that the average balance is different from $75, which test would you use?
    1. Z-test of a population mean
    2. Z-test of a population proportion
    3. t-test of a population mean
    4. t-test of  a population proportion

 

 

 

  1. A manager of the credit department for an oil company would like to determine whether the average monthly balance of credit card holders is equal to $75. An auditor selects a random sample of 100 accounts and finds that the average owed is $83.40 with a sample standard deviation of $23.65. If you were to conduct a test to determine whether the average balance is different from $75 and decided to reject the null hypothesis, what conclusion could you draw?
    1. There is not evidence that the average balance is $75.
    2. There is not evidence that the average balance is not $75.
    3. There is evidence that the average balance is $75.
    4. There is evidence that the average balance is not $75.

 

 

 

  1. The marketing manager for an automobile manufacturer is interested in determining the proportion of new compact-car owners who would have purchased a passenger-side inflatable air bag if it had been available for an additional cost of $300. The manager believes from previous information that the proportion is 0.30. Suppose that a survey of 200 new compact-car owners is selected and 79 indicate that they would have purchased the inflatable air bags. If you were to conduct a test to determine whether there is evidence that the proportion is different from 0.30, which test would you use?
    1. Z-test of a population mean
    2. Z-test of a population proportion
    3. t-test of population mean
    4. t-test of  a population proportion

 

 

 

 

 

  1. The marketing manager for an automobile manufacturer is interested in determining the proportion of new compact-car owners who would have purchased a passenger-side inflatable air bag if it had been available for an additional cost of $300. The manager believes from previous information that the proportion is 0.30. Suppose that a survey of 200 new compact-car owners is selected and 79 indicate that they would have purchased the inflatable air bags. If you were to conduct a test to determine whether there is evidence that the proportion is different from 0.30 and decided not to reject the null hypothesis, what conclusion could you draw?
    1. There is sufficient evidence that the proportion is 0.30.
    2. There is not sufficient evidence that the proportion is 0.30.
    3. There is sufficient evidence that the proportion is 0.30.
    4. There is not sufficient evidence that the proportion is not 0.30.

 

 

 

 

TABLE 9-1

 

Microsoft Excel was used on a set of data involving the number of parasites found on 46 Monarch butterflies captured in Pismo Beach State Park. A biologist wants to know if the mean number of parasites per butterfly is over 20. She will make her decision using a test with a level of significance of 0.10.  The following information was extracted from the Microsoft Excel output for the sample of 46 Monarch butterflies:

n = 46;  Arithmetic Mean = 28.00;  Standard Deviation = 25.92;  Standard Error = 3.82; 

Null Hypothesis: a = 0.10;  df = 45;  T Test Statistic = 2.09;

One-Tailed Test Upper Critical Value = 1.3006;  p-value = 0.021;  Decision = Reject.   

 

  1. Referring to Table 9-1, the parameter the biologist is interested in is:
    1. the mean number of butterflies in Pismo Beach State Park.
    2. the mean number of parasites on these 46 butterflies.
    3. the mean number of parasites on Monarch butterflies in Pismo Beach State Park.
    4. the proportion of butterflies with parasites.

 

 

 

  1. Referring to Table 9-1, state the alternative hypothesis for this study.

 

 

  1. Referring to Table 9-1, what critical value should the biologist use to determine the rejection region?
    1. 1.6794
    2. 1.3011
    3. 1.3006
    4. 0.6800

 

 

 

  1. True or False: Referring to Table 9-1, the null hypothesis would be rejected.

 

 

 

  1. True or False: Referring to Table 9-1, the null hypothesis would be rejected if a 4% probability of committing a Type I error is allowed.

 

 

 

  1. True or False: Referring to Table 9-1, the null hypothesis would be rejected if a 1% probability of committing a Type I error is allowed.

 

 

 

  1. Referring to Table 9-1, the lowest level of significance at which the null hypothesis can be rejected is ______.

 

 

  1. True or False: Referring to Table 9-1, the evidence proves beyond a doubt that the mean number of parasites on butterflies in Pismo Beach State Park is over 20.

 

 

 

  1. True of False: Referring to Table 9-1, the biologist can conclude that there is sufficient evidence to show that the average number of parasites per butterfly is over 20 using a level of significance of 0.10.

 

 

 

  1. True or False: Referring to Table 9-1, the biologist can conclude that there is sufficient evidence to show that the average number of parasites per butterfly is over 20 with no more than a 5% probability of incorrectly rejecting the true null hypothesis.

 

 

 

  1. True or False: Referring to Table 9-1, the biologist can conclude that there is sufficient evidence to show that the average number of parasites per butterfly is over 20 with no more than a 1% probability of incorrectly rejecting the true null hypothesis.

 

 

 

  1. True or False: Referring to Table 9-1, the value of  is 0.90.

 

 

 

  1. True or False: Referring to Table 9-1, if these data were used to perform a two-tailed test, the p-value would be 0.042.

 

 

 

  1. Referring to Table 9-1, the power of the test is _____ if the mean number of parasites per butterfly on Monarch butterflies in Pismo Beach State Park is 18 using a 0.1 level of significance and assuming that the population standard deviation is 25.92.

 

 

 

 

  1. Referring to Table 9-1, the probability of committing a Type II error is _____ if the mean number of parasites per butterfly on Monarch butterflies in Pismo Beach State Park is 18 using a 0.1 level of significance and assuming that the population standard deviation is 25.92.

 

 

  1. Referring to Table 9-1, the power of the test is _____ if the mean number of parasites per butterfly on Monarch butterflies in Pismo Beach State Park is 24 using a 0.1 level of significance and assuming that the population standard deviation is 25.92.

 

  1. Referring to Table 9-1, the probability of committing a Type II error is _____ if the mean number of parasites per butterfly on Monarch butterflies in Pismo Beach State Park is 24 using a 0.1 level of significance and assuming that the population standard deviation is 25.92.

 

 

  1. Referring to Table 9-1, the power of the test is _____ if the mean number of parasites per butterfly on Monarch butterflies in Pismo Beach State Park is 30 using a 0.1 level of significance and assuming that the population standard deviation is 25.92.

 

 

  1. Referring to Table 9-1, the probability of committing a Type II error is _____ if the mean number of parasites per butterfly on Monarch butterflies in Pismo Beach State Park is 30 using a 0.1 level of significance and assuming that the population standard deviation is 25.92.

 

  1. Referring to Table 9-1, the power of the test is _____ if the mean number of parasites per butterfly on Monarch butterflies in Pismo Beach State Park is 18 using a 0.05 level of significance and assuming that the population standard deviation is 25.92.

 

 

  1. Referring to Table 9-1, the probability of committing a Type II error is _____ if the mean number of parasites per butterfly on Monarch butterflies in Pismo Beach State Park is 18 using a 0.05 level of significance and assuming that the population standard deviation is 25.92.

 

 

 

  1. Referring to Table 9-1, the power of the test is _____ if the mean number of parasites per butterfly on Monarch butterflies in Pismo Beach State Park is 24 using a 0.05 level of significance and assuming that the population standard deviation is 25.92.

 

 

  1. Referring to Table 9-1, the probability of committing a Type II error is _____ if the mean number of parasites per butterfly on Monarch butterflies in Pismo Beach State Park is 24 using a 0.05 level of significance and assuming that the population standard deviation is 25.92.

 

 

  1. Referring to Table 9-1, the power of the test is _____ if the mean number of parasites per butterfly on Monarch butterflies in Pismo Beach State Park is 30 using a 0.05 level of significance and assuming that the population standard deviation is 25.92.

 

 

  1. Referring to Table 9-1, the probability of committing a Type II error is _____ if the mean number of parasites per butterfly on Monarch butterflies in Pismo Beach State Park is 30 using a 0.05 level of significance and assuming that the population standard deviation is 25.92.

 

 

  1. True or False: Suppose, in testing a hypothesis about a proportion, the p-value is computed to be 0.043. The null hypothesis should be rejected if the chosen level of significance is 0.05.

 

 

 

  1. True or False: Suppose, in testing a hypothesis about a proportion, the p-value is computed to be 0.034. The null hypothesis should be rejected if the chosen level of significance is 0.01.

 

 

 

  1. True or False: Suppose, in testing a hypothesis about a proportion, the Z test statistic is computed to be 2.04. The null hypothesis should be rejected if the chosen level of significance is 0.01 and a two-tailed test is used.

 

 

 

  1. True or False: In testing a hypothesis, statements for the null and alternative hypotheses as well as the selection of the level of significance should precede the collection and examination of the data.

 

 

 

  1. True or False: The test statistic measures how close the computed sample statistic has come to the hypothesized population parameter.

 

 

 

  1. True or False: The statement of the null hypothesis always contains an equality.

 

 

 

  1. True or False: The larger is the p-value, the more likely one is to reject the null hypothesis.

 

 

 

  1. True or False: The smaller is the p-value, the stronger is the evidence against the null hypothesis.

 

 

 

  1. True or False: A sample is used to obtain a 95% confidence interval for the mean of a population. The confidence interval goes from 15 to 19. If the same sample had been used to test the null hypothesis that the mean of the population is equal to 20 versus the alternative hypothesis that the mean of the population differs from 20, the null hypothesis could be rejected at a level of significance of 0.05.

 

 

 

  1. True or False: A sample is used to obtain a 95% confidence interval for the mean of a population. The confidence interval goes from 15 to 19. If the same sample had been used to test the null hypothesis that the mean of the population is equal to 18 versus the alternative hypothesis that the mean of the population differs from 18, the null hypothesis could be rejected at a level of significance of 0.05.

 

 

 

  1. True or False: A sample is used to obtain a 95% confidence interval for the mean of a population. The confidence interval goes from 15 to 19. If the same sample had been used to test the null hypothesis that the mean of the population is equal to 20 versus the alternative hypothesis that the mean of the population differs from 20, the null hypothesis could be rejected at a level of significance of 0.10.

 

 

 

  1. True or False: A sample is used to obtain a 95% confidence interval for the mean of a population. The confidence interval goes from 15 to 19. If the same sample had been used to test the null hypothesis that the mean of the population is equal to 20 versus the alternative hypothesis that the mean of the population differs from 20, the null hypothesis could be rejected at a level of significance of 0.02.

 

 

 

 

  1. True or False: A sample is used to obtain a 95% confidence interval for the mean of a population. The confidence interval goes from 15 to 19. If the same sample had been used to test the null hypothesis that the mean of the population is equal to 20 versus the alternative hypothesis that the mean of the population differs from 20, the null hypothesis could be accepted at a level of significance of 0.02.

 

 

TABLE 9-2 

 

A student claims that he can correctly identify whether a person is a business major or an agriculture major by the way the person dresses. Suppose in actuality that if someone is a business major, he can correctly identify that person as a business major 87% of the time.  When a person is an agriculture major, the student will incorrectly identify that person as a business major 16% of the time. Presented with one person and asked to identify the major of this person (who is either a business or agriculture major), he considers this to be a hypothesis test with the null hypothesis being that the person is a business major and the alternative that the person is an agriculture major.

 

  1. Referring to Table 9-2, what would be a Type I error?
    1. Saying that the person is a business major when in fact the person is a business major.
    2. Saying that the person is a business major when in fact the person is an agriculture major.
    3. Saying that the person is an agriculture major when in fact the person is a business major.
    4. Saying that the person is an agriculture major when in fact the person is an agriculture major.

 

 

 

  1. Referring to Table 9-2, what would be a Type II error?
    1. Saying that the person is a business major when in fact the person is a business major.
    2. Saying that the person is a business major when in fact the person is an agriculture major.
    3. Saying that the person is an agriculture major when in fact the person is a business major.
    4. Saying that the person is an agriculture major when in fact the person is an agriculture major.

 

 

 

  1. Referring to Table 9-2, what is the “actual level of significance” of the test?
    1. 0.13
    2. 0.16
    3. 0.84
    4. 0.87

 

 

 

  1. Referring to Table 9-2, what is the “actual confidence coefficient”?
    1. 0.13
    2. 0.16
    3. 0.84
    4. 0.87

 

 

 

  1. Referring to Table 9-2, what is the value of ?
    1. 0.13
    2. 0.16
    3. 0.84
    4. 0.87

 

 

 

  1. Referring to Table 9-2, what is the value of ?
    1. 0.13
    2. 0.16
    3. 0.84
    4. 0.87

 

 

 

  1. Referring to Table 9-2, what is the power of the test?
    1. 0.13
    2. 0.16
    3. 0.84
    4. 0.87

 

 

 

 

 

TABLE 9-3

 

An appliance manufacturer claims to have developed a compact microwave oven that consumes an average of no more than 250 W. From previous studies, it is believed that power consumption for microwave ovens is normally distributed with a standard deviation of 15 W. A consumer group has decided to try to discover if the claim appears true. They take a sample of 20 microwave ovens and find that they consume an average of 257.3 W.

 

  1. Referring to Table 9-3, the population of interest is
    1. the power consumption in the 20 microwave ovens.
    2. the power consumption in all such microwave ovens.
    3. the mean power consumption in the 20 microwave ovens.
    4. the mean power consumption in all such microwave ovens.

 

 

 

  1. Referring to Table 9-3, the parameter of interest is
    1. the mean power consumption of the 20 microwave ovens.
    2. the mean power consumption of all such microwave ovens.
    3. 250
    4. 257.3

 

 

 

  1. Referring to Table 9-3, the appropriate hypotheses to determine if the manufacturer's claim appears reasonable are:

 

 

 

  1. Referring to Table 9-3, for a test with a level of significance of 0.05, the critical value would be ________. 

 

 

  1. Referring to Table 9-3, the value of the test statistic is ________.

 

 

  1. Referring to Table 9-3, the p-value of the test is ________.

 

 

  1. True or False: Referring to Table 9-3, for this test to be valid, it is necessary that the power consumption for microwave ovens has a normal distribution.

 

 

 

  1. True or False: Referring to Table 9-3, the null hypothesis will be rejected at 5% level of significance.

 

 

 

  1. True or False: Referring to Table 9-3, the null hypothesis will be rejected at 1% level of significance.

 

 

 

 

  1. True or False: Referring to Table 9-3, the consumer group can conclude that there is enough evidence to prove that the manufacturer’s claim is not true when allowing for a 5% probability of committing a type I error.

 

 

  1. Referring to Table 9-3, what is the power of the test if the average power consumption of all such microwave ovens is in fact 257.3 W using a 0.05 level of significance?

 

 

  1. Referring to Table 9-3, what is the probability of making a Type II error if the average power consumption of all such microwave ovens is in fact 257.3 W using a 0.05 level of significance?

 

 

  1. Referring to Table 9-3, what is the power of the test if the average power consumption of all such microwave ovens is in fact 248 W using a 0.05 level of significance?

 

 

  1. Referring to Table 9-3, what is the probability of making a Type II error if the average power consumption of all such microwave ovens is in fact 248 W using a 0.05 level of significance?

 

 

  1. Referring to Table 9-3, what is the power of the test if the average power consumption of all such microwave ovens is in fact 257.3 W using a 0.10 level of significance?

 

 

  1. Referring to Table 9-3, what is the probability of making a Type II error if the average power consumption of all such microwave ovens is in fact 257.3 W using a 0.10 level of significance?

 

 

  1. Referring to Table 9-3, what is the power of the test if the average power consumption of all such microwave ovens is in fact 248 W using a 0.10 level of significance?

 

 

  1. Referring to Table 9-3, what is the probability of making a Type II error if the average power consumption of all such microwave ovens is in fact 248 W using a 0.10 level of significance?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

TABLE 9-4

 

A drug company is considering marketing a new local anesthetic. The effective time of the anesthetic the drug company is currently producing has a normal distribution with an average of 7.4 minutes with a standard deviation of 1.2 minutes. The chemistry of the new anesthetic is such that the effective time should be normal with the same standard deviation, but the mean effective time may be lower. If it is lower, the drug company will market the new anesthetic; otherwise, they will continue to produce the older one. A sample of size 36 results in a sample mean of 7.1.  A hypothesis test will be done to help make the decision.

 

  1. Referring to Table 9-4, the appropriate hypotheses are:

  

 

 

  1. Referring to Table 9-4, for a test with a level of significance of 0.10, the critical value would be ________.

 

 

  1. Referring to Table 9-4, the value of the test statistic is ________.

 

 

  1. Referring to Table 9-4, the p-value of the test is ________.

 

 

  1. True or False: Referring to Table 9-4, the null hypothesis will be rejected with a level of significance of 0.10.

 

 

 

  1. True or False: Referring to Table 9-4, if the level of significance had been chosen as 0.05, the null hypothesis would be rejected.

 

 

 

  1. True or False: Referring to Table 9-4, if the level of significance had been chosen as 0.05, the company would market the new anesthetic.

 

 

  1. Referring to Table 9-4, what is the power of the test if the average effective time of the anesthetic is 7.0 using a 0.05 level of significance?

 

 

  1. Referring to Table 9-4, what is the probability of making a Type II error if the average effective time of the anesthetic is 7.0 using a 0.05 level of significance?

 

 

  1. Referring to Table 9-4, what is the power of the test if the average effective time of the anesthetic is 7.5 using a 0.05 level of significance?

 

 

  1. Referring to Table 9-4, what is the probability of making a Type II error if the average effective time of the anesthetic is 7.5 using a 0.05 level of significance?

 

 

  1. Referring to Table 9-4, what is the power of the test if the average effective time of the anesthetic is 7.0 using a 0.10 level of significance?

 

 

  1. Referring to Table 9-4, what is the probability of making a Type II error if the average effective time of the anesthetic is 7.0 using a 0.10 level of significance?

 

 

  1. Referring to Table 9-4, what is the power of the test if the average effective time of the anesthetic is 7.5 using a 0.10 level of significance?

 

 

  1. Referring to Table 9-4, what is the probability of making a Type II error if the average effective time of the anesthetic is 7.5 using a 0.10 level of significance?

 

 

TABLE 9-5

 

A bank tests the null hypothesis that the mean age of the bank's mortgage holders is less than or equal to 45, versus an alternative that the mean age is greater than 45. They take a sample and calculate a p-value of 0.0202.

 

  1. True or False: Referring to Table 9-5, the null hypothesis would be rejected at a significance level of  = 0.05.

 

 

 

  1. True or False: Referring to Table 9-5, the null hypothesis would be rejected at a significance level of  = 0.01.

 

 

 

  1. True or False: Referring to Table 9-5, the bank can conclude that the average age is greater than 45 at a significance level of  = 0.01.

 

 

 

  1. Referring to Table 9-5, if the same sample was used to test the opposite one-tailed test, what would be that test's p-value?
    1. 0.0202
    2. 0.0404
    3. 0.9596
    4. 0.9798

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

TABLE 9-6

 

The quality control engineer for a furniture manufacturer is interested in the mean amount of force necessary to produce cracks in stressed oak furniture. She performs a two-tailed test of the null hypothesis that the mean for the stressed oak furniture is 650. The calculated value of the Z test statistic is a positive number that leads to a p-value of 0.080 for the test.

 

  1. True or False: Referring to Table 9-6, if the test is performed with a level of significance of 0.10, the null hypothesis would be rejected.

 

 

 

  1. True or False: Referring to Table 9-6, if the test is performed with a level of significance of 0.10, the engineer can conclude that the mean amount of force necessary to produce cracks in stressed oak furniture is 650.

 

 

  1. True or False: Referring to Table 9-6, if the test is performed with a level of significance of 0.05, the null hypothesis would be rejected.

 

 

  1. True or False: Referring to Table 9-6, if the test is performed with a level of significance of 0.05, the engineer can conclude that the mean amount of force necessary to produce cracks in stressed oak furniture is 650.

 

 

 

 

  1. True or False: Referring to Table 9-6, suppose the engineer had decided that the alternative hypothesis to test was that the mean was greater than 650. Then if the test is performed with a level of significance of 0.10, the null hypothesis would be rejected.

 

 

 

  1. Referring to Table 9-6, suppose the engineer had decided that the alternative hypothesis to test was that the mean was greater than 650. What would be the p-value of this one-tailed test?
    1. 0.040
    2. 0.160
    3. 0.840
    4. 0.960

 

 

 

  1. Referring to Table 9-6, suppose the engineer had decided that the alternative hypothesis to test was that the mean was less than 650. What would be the p-value of this one-tailed test?
    1. 0.040
    2. 0.160
    3. 0.840
    4. 0.960

 

 

 

  1. True or False: Referring to Table 9-6, suppose the engineer had decided that the alternative hypothesis to test was that the mean was less than 650. Then if the test is performed with a level of significance of 0.10, the null hypothesis would be rejected.

 

 

 

 

 

 

TABLE 9-7

A major home improvement store conducted its biggest brand recognition campaign in the company’s history.  A series of new television advertisements featuring well-known entertainers and sports figures were launched.  A key metric for the success of television advertisements is the proportion of viewers who “like the ads a lot”.  A study of 1,189 adults who viewed the ads reported that 230 indicated that they “like the ads a lot.”  The percentage of a typical television advertisement receiving the “like the ads a lot” score is believed to be 22%.   Company officials wanted to know if there is evidence that the series of television advertisements are less successful than the typical ad (i.e. if there is evidence that the population proportion of “like the ads a lot” for the company’s ads is less than 0.22) at a 0.01 level of significance.

 

  1. Referring to Table 9-7, the parameter the company officials is interested in is:
    1. the mean number of viewers who “like the ads a lot”.
    2. the total number of viewers who “like the ads a lot”.
    3. the mean number of company officials who “like the ads a lot”.
    4. the proportion of viewers who “like the ads a lot”.

 

 

 

  1. Referring to Table 9-7, state the null hypothesis for this study.

 

 

  1. Referring to Table 9-7, state the alternative hypothesis for this study.

ANSWER:

 

 

  1. Referring to Table 9-7, what critical value should the company officials use to determine the rejection region?

 

 

  1. Referring to Table 9-7, the null hypothesis will be rejected if the test statistics is
    1. greater than 2.3263
    2. less than 2.3263
    3. greater than ?2.3263
    4. less than ?2.3263

 

 

 

  1. True or False: Referring to Table 9-7, the null hypothesis would be rejected.

 

 

 

  1. Referring to Table 9-7, the lowest level of significance at which the null hypothesis can be rejected is ______.

 

 

  1. Referring to Table 9-7, the largest level of significance at which the null hypothesis will not be rejected is ______.

 

 

  1. True of False: Referring to Table 9-7, the company officials can conclude that there is sufficient evidence to show that the series of television advertisements are less successful than the typical ad using a level of significance of 0.01.

 

 

 

  1. True or False: Referring to Table 9-7, the company officials can conclude that there is sufficient evidence to show that the series of television advertisements are less successful than the typical ad using a level of significance of 0.05.

 

 

 

  1. True or False: Referring to Table 9-7, the value of  is 0.90.

 

 

 

  1. Referring to Table 9-7, what will be the p-value if these data were used to perform a two-tailed test?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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