Exam 9: Introduction to Hypothesis Testing

Because of the complex nature of the U.S.income tax system,many people have questions for the Internal Revenue Service (IRS).Yet,an article published by the Detroit Free Press entitled "Assistance: IRS Help Centers Give the Wrong Information" discusses the propensity of IRS staff employees to give incorrect tax information to tax-payers who call with questions.Then IRS Inspector General Pamela Gardiner told a Senate subcommittee that "the IRS employees at 400 taxpayer assistance centers nationwide encountered 8.5 million taxpayers face-to-face last year.The problem: When inspector general auditors posing as taxpayers asked them to answer tax questions,the answers were right 69% of the time." Suppose an independent commission was formed to test whether the 0.69 accuracy rate is correct or whether it is actually higher or lower.The commission has randomly selected n = 180 tax returns that were completed by IRS assistance employees and found that 105 of the returns were accurately completed. State the appropriate null and alternative hypotheses.

The director of a state agency believes that the average starting salary for clerical employees in the state is less than $30,000 per year.To test her hypothesis,she has collected a simple random sample of 100 starting clerical salaries from across the state and found that the sample mean is $29,750.Assuming the population standard deviation is known to be $2,500 and the significance level for the test is to be 0.05,what is the critical value (stated in dollars)?

A recent article in The Wall Street Journal entitled "As Identity Theft Moves Online,Crime Rings Mimic Big Business" states that 39% of the consumer scam complaints by American consumers are about identity theft.Suppose a random sample of 90 complaints is obtained.Of these complaints,40 were regarding identity theft.Based on these sample data,what conclusion should be reached about the statement made in The Wall Street Journal? (Test using α= 0.10. )

To calculate beta requires making a "what if" assumption about the true population parameter,where the "what-if" value is one that would cause the null hypothesis to be false.

In a two-tailed hypothesis test for a population mean,an increase in the sample size will:

If the p value is less than α in a two-tailed test,

In hypothesis testing,the null hypothesis should contain the equality sign.

A cell phone company believes that 90 percent of their customers are satisfied.They survey a sample of n = 100 customers and find that 82 say they are satisfied.In calculating the standard error of the sampling distribution (σ_p)the proportion to use is 0.82.

A major issue facing many states is whether to legalize casino gambling.Suppose the governor of one state believes that more than 55% of the state's registered voters would favor some form of legal casino gambling.However,before backing a proposal to allow such gambling,the governor has instructed his aides to conduct a statistical test on the issue.To do this,the aides have hired a consulting firm to survey a simple random sample of 300 voters in the state.Of these 300 voters,175 actually favored legalized gambling. Assuming that a significance level of 0.05 is used,what conclusion should the governor reach based on these sample data?

Swift is the holding company for Swift Transportation Co. ,Inc. ,a truckload carrier headquartered in Phoenix,Arizona.Swift operates the largest truckload fleet in the United States.Before Swift switched to its current computer-based billing system,the average payment time from customers was approximately 40 days.Suppose before purchasing the present billing system,it performed a test by examining a random sample of 24 invoices to see if the system would reduce the average billing time.The sample indicates that the average payment time is 38.7 days. The company that created the billing system indicates that the system would reduce the average billing time to less than 40 days.Conduct a hypothesis test to determine if the new computer-based billing system would reduce the average billing time to less than 40 days.Assume the standard deviation is known to be 6 days.Use a significance level of 0.025.

A company that sells an online course aimed at helping high-school students improve their SAT scores has claimed that SAT scores will improve by more than 90 points on average if students successfully complete the course.To test this,a national school counseling organization plans to select a random sample of n = 100 students who have previously taken the SAT test.These students will take the company's course and then retake the SAT test.Assuming that the population standard deviation for improvement in test scores is thought to be 30 points and the level of significance for the hypothesis test is 0.05,what is the probability that the counseling organization will incorrectly "accept" the null hypothesis when,in fact,the true mean increase is actually 95 points?

The significance level in a hypothesis test corresponds to the maximum probability that a Type I error will be committed.

Mike runs for the president of the student government and is interested to know whether the proportion of the student body in favor of him is significantly more than 50 percent.A random sample of 100 students was taken.Fifty-five of them favored Mike.At a 0.05 level of significance,it can be concluded that the proportion of the students in favor of Mike

In a two-tailed hypothesis test the area in each tail of the rejection region is equal to α.

In a hypothesis test,increasing the sample size will generally result in a smaller chance of making a Type I error since sampling error is likely to be reduced.

Which of the following would be an appropriate null hypothesis?

A cell phone company believes that 90 percent of its customers are satisfied with their service.They survey n = 30 customers.Based on this,it is acceptable to assume the sample distribution is normally distributed.

For the following hypothesis test: With n= 64 and p= 0.42,state the decision rule in terms of the critical value of the test statistic

A report recently submitted to the managing partner for a market research company stated "the hypothesis test may have resulted in either a Type I or a Type II error.We won't know which one occurred until later." This statement is one that we might correctly make for any hypothesis that we have conducted.

For the following hypothesis test: With n = 80,σ = 9,and = 47.1,state the decision rule in terms of the critical value of the test statistic.