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

Suppose,in testing a hypothesis about a mean,the p-value is computed to be 0.034.The null hypothesis should be rejected if the chosen level of significance is 0.01.

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?

"What conclusions and interpretations can you reach from the results of the hypothesis test?" is not an important question to ask when performing a hypothesis test.

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 = 0.01.

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,if the test is performed with a level of significance of 0.05,the null hypothesis would be rejected.

Referring to Table 9.3,the value of the test statistic is .

A proper methodology in performing hypothesis tests is to ask whether a random sample can be selected from the population of interest.

SCENARIO 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 Scenario 9-4,the appropriate hypotheses are:

Suppose we wish to test H₀: $\le$ versus H₁: > 47.What will result if we conclude that the mean is greater than 47 when its true value is really 52?

SCENARIO 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 Scenario 9-4,the value of the test statistic is .

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

A Type I error is committed when

Which of the following would be an appropriate alternative hypothesis?

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,what critical value should the company officials use to determine the rejection region?

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,state the alternative hypothesis for this study.

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

SCENARIO 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 Scenario 9-3,the parameter of interest is

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 parameter the company officials is interested in is:

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 value of the probability of committing a Type II error $\beta$ is 0.95.

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,which of the following best describes the Type I error?