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

True or False: You should report only the results of hypothesis tests that show statistical significance and omit those for which there is insufficient evidence in the findings.

True or False: For a given level of significance, if the sample size is increased but the summary statistics remain the same, the probability of committing a Type II error will increase.

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 alternative hypothesis for this study.

Referring to Scenario 9-6, suppose the engineer had decided that the alternative hypothesis to Test was that the mean was less than 650.What would be the p-value of this one-tail test?

A Type I error is committed when

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 would be a Type II error?

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 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 5% probability of incorrectly rejecting the true null hypothesis.

A manager of the credit department for an oil company would like to determine whether the mean Monthly balance of credit card holders is equal to $75.An auditor selects a random sample of 100 Accounts and finds that the mean owed is $83.40 with a sample standard deviation of $23.65.If You wanted to test whether the mean balance is different from $75 and decided to reject the null Hypothesis, what conclusion could you reach?

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, for this test to be valid, it is necessary that the power consumption for microwave ovens has a normal distribution.

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 decision on the hypothesis Test using a 5% level of significance is:

Which of the following would be an appropriate alternative hypothesis?

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

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 9-5 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 Scenario 9-5, the null hypothesis would be rejected at a significance level of

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

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 10% probability of committing a Type I error is allowed.