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,the null hypothesis would be rejected if a 10% probability of committing a Type I error is allowed.

You have created a 95% confidence interval for ? with the result 10 $\le$$\mu$ $\le$ 15 .What decision will you make if you test H₀ : ? $\neq$ 16 versus H₁ : ? $\neq$ 16 at ? = 0.05?

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,the lowest level of significance at which the null hypothesis can be rejected is .

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.

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: X = 52,S = 22.Suppose the alternative you wanted to test was H₁ : $\lt$ 60 .State the correct rejection region for = 0.05.

If,as a result of a hypothesis test,you reject the null hypothesis when it is false,then you have committed

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?

Which of the following would be an appropriate null hypothesis?

SCENARIO 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 Scenario 9-5,the null hypothesis would be rejected at a significance level of α = 0.05.

SCENARIO 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 Scenario 9-1,the null hypothesis would be rejected.

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 H}0 ^{should be rejected at the} (a)α= 0.10, (b)α= 0.05,and (c)α= 0.01 level of Type I error?

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.State the test of hypothesis that is of interest to the pizza chain.

SCENARIO 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 Scenario 9-5,if the same sample was used to test the opposite one-tail test,what would be that test's p-value?

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 brain.It conducts a telephone poll of 300 randomly selected households in the area and finds that 96 have a favorable view.The value of the test statistic in this problem is approximately equal to:

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 0.02.

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

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 at a 0.01 level of significance. -Referring to Scenario 9-7,the lowest level of significance at which the null hypothesis can be rejected is .

SCENARIO 9-10 A manufacturer produces light bulbs that have a mean life of at least 500 hours when the production process is working properly.Based on past experience,the population standard deviation is 50 hours and the light bulb life is normally distributed.The operations manager stops the production process if there is evidence that the population mean light bulb life is below 500 hours. -Referring to Scenario 9-10,if you select a sample of 100 light bulbs and are willing to have a level of significance of 0.01,the probability of the operations manager failing to stop the process if the population mean bulb life is 490 hours is .

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 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. -Referring to Scenario 9-6,suppose the engineer had decided that the alternative hypothesis to test was that the mean was greater than 650.Then if the test is performed with a level of significance of 0.05,the null hypothesis would be rejected.