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

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 parameter the manager is interested in is

If a researcher does not reject a false null hypothesis,she has made a(n)________ 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: -Referring to Table 9-1,state the alternative hypothesis for this study.

You have created a 95% confidence interval for μ with the result 10 ≤ μ ≤ 15.What decision will you make if we test H₀: μ = 16 versus H₁: μ ≠ 16 at α = 0.10?

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 a 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 size of 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,the appropriate hypotheses are

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 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 Table 9-8,what will be the p-value if these data were used to perform a two-tail test?

If you know that the level of significance (α)of a test is 5%,you can tell that the probability of committing a Type II error (β)is

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 at a 0.01 level of significance. -True or False: Referring to Table 9-7,the null hypothesis would be rejected.

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 value of the test statistic is ________.

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

Which of the following would be an appropriate null hypothesis?

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

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 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. -True or False: Referring to Table 9-8,the company officials can conclude that there is sufficient evidence that the conversion rate at the company's website has increased using a level of significance of 0.05.

The symbol for the level of significance of a statistical test is

The symbol for the power of a statistical test 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 a mean of 257.3 W. -True or False: Referring to Table 9-3,the null hypothesis will be rejected at 5% level of significance.

Suppose you want to test H₀ : μ ≥ 30 versus H₁ : μ < 30.Which of the following possible sample results based on a sample size of 36 gives the strongest evidence to reject H₀ in favor of H₁?

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.

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 value of α?

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