Exam 9: Fundamentals of Hypothesis Testing: One-Sample Tests

SCENARIO 9-9 The president of a university claimed that the entering class this year appeared to be larger than the entering class from previous years but their mean SAT score is lower than previous years.He took a sample of 20 of this year's entering students and found that their mean SAT score is 1,501 with a standard deviation of 53.The university's record indicates that the mean SAT score for entering students from previous years is 1,520.He wants to find out if his claim is supported by the evidence at a 5% level of significance. -Referring to Scenario 9-9, which of the following best describes the Type II error?

The marketing manager for an automobile manufacturer is interested in determining the proportion of new compact-car owners who would have purchased a GPS navigation system 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 GPS navigation system.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 reach?

True or False In setting up a hypothesis test, you consider the null hypothesis as stating the status quo claim.

SCENARIO 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. -Referring to Scenario 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.

In a hypothesis test, it is irrelevant whether the test is a one-tail or two-tail test.

Which of the following would be an appropriate alternative hypothesis?

SCENARIO 9-6 The quality control engineer for a furniture manufacturer is interested in the mean amount of force in pounds necessary to produce cracks in stressed oak furniture.She performs a two-tail test of the null hypothesis that the mean for the stressed oak furniture is 650 pounds.The calculated value of the Z test statistic is a positive number that leads to a p-value of 0.080 for the test. -Referring to Scenario 9-6, suppose the engineer had decided that the alternative hypothesis to test was that the mean was less than 650 pounds.Then if the test is performed with a level of significance of 0.05, the null hypothesis would be rejected.

SCENARIO 9-3 An appliance manufacturer claims to have developed a compact microwave oven that consumes a mean of no more than 250 W.From previous studies, it is believed that power consumption for microwave ovens is normally distributed with a population 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 a mean of 257.3 W. -Referring to Scenario 9-3, the appropriate hypotheses to determine if the manufacturer's claim appears reasonable are:

SCENARIO 9-9 The president of a university claimed that the entering class this year appeared to be larger than the entering class from previous years but their mean SAT score is lower than previous years.He took a sample of 20 of this year's entering students and found that their mean SAT score is 1,501 with a standard deviation of 53.The university's record indicates that the mean SAT score for entering students from previous years is 1,520.He wants to find out if his claim is supported by the evidence at a 5% level of significance. -Referring to Scenario 9-9, the president can conclude that there is sufficient evidence to show that the mean SAT score of the entering class this year is lower than previous years with no more than a 5% probability of incorrectly rejecting the true null hypothesis.

SCENARIO 9-3 An appliance manufacturer claims to have developed a compact microwave oven that consumes a mean of no more than 250 W.From previous studies, it is believed that power consumption for microwave ovens is normally distributed with a population 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 a mean of 257.3 W. -Referring to Scenario 9-3, the population of interest is

How many tissues should the Kimberly Clark Corporation package of Kleenex contain? Researchers determined that 60 tissues is the mean 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: Using the sample information provided, calculate the value of the test statistic.

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:

If a researcher does not reject a false null hypothesis, she has made a _______error.

SCENARIO 9-9 The president of a university claimed that the entering class this year appeared to be larger than the entering class from previous years but their mean SAT score is lower than previous years.He took a sample of 20 of this year's entering students and found that their mean SAT score is 1,501 with a standard deviation of 53.The university's record indicates that the mean SAT score for entering students from previous years is 1,520.He wants to find out if his claim is supported by the evidence at a 5% level of significance. -Referring to Scenario 9-9, the null hypothesis would be rejected if a 1% probability of committing a Type I error is allowed.

A pizza 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 have a favorable view of its brand.It conducts a telephone poll of 300 randomly selected households in the area and finds that 96 have a favorable view.The p-value associated with the test statistic in this problem is approximately equal to:

SCENARIO 9-8 One of the biggest issues facing e-retailers is the ability to turn browsers into buyers.This is measured by the conversion rate, the percentage of browsers who buy something in their visit to a site.The conversion rate for a company's website was 10.1%.The website at the company was redesigned in an attempt to increase its conversion rates.A sample of 200 browsers at the redesigned site was selected.Suppose that 24 browsers made a purchase.The company officials would like to know if there is evidence of an increase in conversion rate at the 5% level of significance. -Referring to Scenario 9-8, what will be the p-value if these data were used to perform a two-tail test?

In conducting research, you should document both good and bad results.

SCENARIO 9-9 The president of a university claimed that the entering class this year appeared to be larger than the entering class from previous years but their mean SAT score is lower than previous years.He took a sample of 20 of this year's entering students and found that their mean SAT score is 1,501 with a standard deviation of 53.The university's record indicates that the mean SAT score for entering students from previous years is 1,520.He wants to find out if his claim is supported by the evidence at a 5% level of significance. -Referring to Scenario 9-9, the president can conclude that there is sufficient evidence to show that the mean SAT score of the entering class this year is lower than previous years with no more than a 10% probability of incorrectly rejecting the true null hypothesis.

You know that the level of significance of a test is 5%, you can tell that the probability of committing a Type II error is

A manager of the credit department for an oil company would like to determine whether the mean monthly balance of credit card holders is equal to $75.An auditor selects a random sample of 100 accounts and finds that the mean owed is $83.40 with a sample standard deviation of $23.65.If you wanted to test whether the mean balance is different from $75 and decided to reject the null hypothesis, what conclusion could you reach?