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

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

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.

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. -True or False: Referring to Scenario 9-9, the president can conclude that the mean SAT score of the entering class this year is lower than previous years using a level of significance of 0.10.

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 (i.e.if there is evidence that the population proportion of "like the ads a lot" for the company's ads is less than -Referring to Scenario 9-7, state the null hypothesis for this study.

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, for a test with a level of significance of 0.10, the critical value would be ________.

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

True or False: The statement of the null hypothesis always contains an equality.

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 pizza chain's conclusion from The hypothesis test using a 5% level of significance 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. -True or False: Referring to Scenario 9-9, the null hypothesis would be rejected.

The power of a statistical test is

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 accepted at a level of significance of 0.01.

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. -True or False: Referring to Scenario 9-9, the null hypothesis would be rejected if a 1% probability of committing a Type I error is allowed.

SCENARIO 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 Scenario 9-2, what is the power of the test?

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. -True or False: Referring to Scenario 9-3, the null hypothesis will be rejected at 5% level of significance.

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:

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?

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. -True or False: Referring to Scenario 9-4, if the level of significance had been chosen as 0.05, the company would market the new anesthetic.