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

The symbol for the probability of committing a Type I error of a statistical test is

For a given level of significance (α), if the sample size n is increased, the probability of a Type II error (β)

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 years, versus an alternative that the mean age is greater than 45 years. They take a sample and calculate a p-value of 0.0202. -Referring to Table 9-5, the null hypothesis would be rejected at a significance level of α = 0.01.

TABLE 9-1 Microsoft Excel was used on a set of data involving the number of defective items found in a random sample of 46 cases of light bulbs produced during a morning shift at a plant. A manager wants to know if the mean number of defective bulbs per case is greater than 20 during the morning shift. 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 cases: -Referring to Table 9-1, the lowest level of significance at which the null hypothesis can be rejected is ________.

TABLE 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 Table 9-9, the null hypothesis would be rejected.

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: = 52, S = 22. Suppose the test statistic does fall in the rejection region at α = 0.05. Which of the following decisions is correct?

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. -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.

TABLE 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 an mean of 257.3 W. -Referring to Table 9-3, the consumer group can conclude that there is enough evidence that the manufacturer's claim is not true when allowing for a 5% probability of committing a Type I error.

TABLE 9-1 Microsoft Excel was used on a set of data involving the number of defective items found in a random sample of 46 cases of light bulbs produced during a morning shift at a plant. A manager wants to know if the mean number of defective bulbs per case is greater than 20 during the morning shift. 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 cases: -You should report only the results of hypothesis tests that show statistical significance and omit those for which there is insufficient evidence in the findings.

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

A major DVD 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 DVD players. It conducts a telephone poll of 300 randomly selected households in the area and finds that 96 have DVD players. The decision on the hypothesis test using a 5% level of significance is:

TABLE 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 an mean of 257.3 W. -Referring to Table 9-3, the appropriate hypotheses to determine if the manufacturer's claim appears reasonable are:

If a researcher rejects a true null hypothesis, she has made a ________ error.

The power of a statistical test is

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 you conclude that H₀ should be rejected at the (a)α = 0.10, (b)α = 0.05, and (c)α = 0.01 level of Type I error?

A major DVD 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 DVD players. It conducts a telephone poll of 300 randomly selected households in the area and finds that 96 have DVD players. The rental chain's conclusion from the hypothesis test using a 5% level of significance is:

TABLE 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 samples 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 Table 9-8, what critical value should the company officials use to determine the rejection region?

TABLE 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 an mean of 257.3 W. -Referring to Table 9-3, the null hypothesis will be rejected at 5% level of significance.

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 greater than 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 have a level of significance at 0.01, what rejection region should she use?

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.