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

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 would be a Type II error?

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-tail 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. -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.

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 p-value of the test is ________.

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

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

If a test of hypothesis has a Type I error probability (α)of 0.01,it means that

If a researcher does not reject a true null hypothesis,she has made a(n)________ decision.

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 9-7 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. -Referring to Table 9-7,the parameter the company officials is interested in 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 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,the parameter the company officials are interested in 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: = 52, S = 22.Suppose the test statistic does fall in the rejection region at α = 0.05.Which of the following conclusions is correct?

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 would be a Type I error?

You have created a 95% confidence interval for μ with the result 10 ≤ μ ≤ 15.What decision will you make if you test H₀: μ = 16 versus H₁: μ ≠ 16 at α = 0.05?

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

True or False: In a hypothesis test,it is irrelevant whether the test is a one-tail or two-tail 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 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,state the null hypothesis for this study.

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.

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 9-1 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,what critical value should the manager use to determine the rejection region?