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

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

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 a mean of 257.3 W. -Referring to Table 9-3,for a test with a level of significance of 0.05,the critical value would be ________.

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 value of the test statistic in this problem is approximately equal to

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 an 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. -Referring to Table 9-2,what is the power of the test?

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 mean 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 normally distributed 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. -Referring to Table 9-4,if the level of significance had been chosen as 0.05,the null hypothesis would be rejected.

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,state the null hypothesis for this study.

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.

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 evidence proves beyond a doubt that the mean number of defective bulbs per case is greater than 20 during the morning shift.

"Is the intended sample size large enough to achieve the desired power of the test for the level of significance chosen?" should be among the questions asked when performing a hypothesis test

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,the largest level of significance at which the null hypothesis will not be rejected is ________.

In instances in which there is insufficient evidence to reject the null hypothesis,you must make it clear that this has proven that the null hypothesis is true.

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 a mean of 257.3 W. -Referring to Table 9-3,the p-value of the test is ________.

It is possible to directly compare the results of a confidence interval estimate to the results obtained by testing a null hypothesis if

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,the value of the probability of committing a Type II error β is 0.95.

An entrepreneur is considering the purchase of a coin-operated laundry.The current owner claims that over the past 5 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 and decide not to reject the null hypothesis,what can you conclude?

Suppose,in testing a hypothesis about a mean,the p-value is computed to be 0.043.The null hypothesis should be rejected if the chosen level of significance is 0.05.

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 evidence proves beyond a doubt that the mean SAT score of the entering class this year is lower than previous years.

A Type I error is committed when

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 was 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 9-9 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 parameter the president is interested in is