1.A production line operation is designed to fill cartons with laundry detergent to a meanweight of 32 ounces. A sample of cartons is periodically selected and weighed to determinewhether underfilling or overfilling is occurring. If the sample data lead to a conclusion ofunderfilling or overfilling, the production line will be shut down and adjusted to obtainproper filling.a. Formulate the null and alternative hypotheses that will help in deciding whether toshut down and adjust the production line.b. Comment on the conclusion and the decision when H0 cannot be rejected.c. Comment on the conclusion and the decision when H0 can be rejected.ConditionH0 True Ha TrueAccept H0Correct Type IIConclusion ErrorConclusionReject H0Type I CorrectError Conclusion2.Nielsen reported that young men in the United States watch 56.2 minutes of prime-time TVdaily (The Wall Street Journal Europe, November 18, 2003). A researcher believes that youngmen in Germany spend more time watching prime-time TV. A sample of German young menwill be selected by the researcher and the time they spend watching TV in one day will berecorded. The sample results will be used to test the following null and alternative hypotheses.a. What is the Type I error in this situation? What are the consequences of making this error?b. What is the Type II error in this situation? What are the consequences of making this error?3.Carpetland salespersons average $8000 per week in sales. Steve Contois, the firm’s vicepresident, proposes a compensation plan with new selling incentives. Steve hopes that theresults of a trial selling period will enable him to conclude that the compensation plan increasesthe average sales per salesperson.a. Develop the appropriate null and alternative hypotheses.b. What is the Type I error in this situation? What are the consequences of making this error?c. What is the Type II error in this situation? What are the consequences of making this error?4.Wall Street securities firms paid out record year-end bonuses of $125,500 per employeefor 2005 (Fortune, February 6, 2006). Suppose we would like to take a sample of employeesat the Jones & Ryan securities firm to see whether the mean year-end bonus isdifferent from the reported mean of $125,500 for the population.a. State the null and alternative hypotheses you would use to test whether the year-endbonuses paid by Jones & Ryan were different from the population mean.b. Suppose a sample of 40 Jones & Ryan employees showed a sample mean year-endbonus of $118,000. Assume a population standard deviation of _ _ $30,000 and computethe p-value.c. With ? _ .05 as the level of significance, what is your conclusion?d. Repeat the preceding hypothesis test using the critical value approach.5.Fowle Marketing Research, Inc., bases charges to a client on the assumption that telephonesurveys can be completed in a mean time of 15 minutes or less. If a longer mean surveytime is necessary, a premium rate is charged. A sample of 35 surveys provided the surveytimes shown in the website file named Fowle. Based upon past studies, the population standarddeviation is assumed known with ? _ 4 minutes. Is the premium rate justified?a. Formulate the null and alternative hypotheses for this application.b. Compute the value of the test statistic.c. What is the p-value?d. At ? _ .01, what is your conclusion?
1.A production line operation is designed to fill cartons with laundry detergent to a meanweight of 32 ounces. A sample of cartons is periodically selected and weighed to determinewhether underfilling or overfilling is occurring. If the sample data lead to a conclusion ofunderfilling or overfilling, the production line will be shut down and adjusted to obtainproper filling.a. Formulate the null and alternative hypotheses that will help in deciding whether toshut down and adjust the production line.b. Comment on the conclusion and the decision when H0 cannot be rejected.c. Comment on the conclusion and the decision when H0 can be rejected.ConditionH0 True Ha TrueAccept H0Correct Type IIConclusion ErrorConclusionReject H0Type I CorrectError Conclusion2.Nielsen reported that young men in the United States watch 56.2 minutes of prime-time TVdaily (The Wall Street Journal Europe, November 18, 2003). A researcher believes that youngmen in Germany spend more time watching prime-time TV. A sample of German young menwill be selected by the researcher and the time they spend watching TV in one day will berecorded. The sample results will be used to test the following null and alternative hypotheses.a. What is the Type I error in this situation? What are the consequences of making this error?b. What is the Type II error in this situation? What are the consequences of making this error?3.Carpetland salespersons average $8000 per week in sales. Steve Contois, the firm’s vicepresident, proposes a compensation plan with new selling incentives. Steve hopes that theresults of a trial selling period will enable him to conclude that the compensation plan increasesthe average sales per salesperson.a. Develop the appropriate null and alternative hypotheses.b. What is the Type I error in this situation? What are the consequences of making this error?c. What is the Type II error in this situation? What are the consequences of making this error?4.Wall Street securities firms paid out record year-end bonuses of $125,500 per employeefor 2005 (Fortune, February 6, 2006). Suppose we would like to take a sample of employeesat the Jones & Ryan securities firm to see whether the mean year-end bonus isdifferent from the reported mean of $125,500 for the population.a. State the null and alternative hypotheses you would use to test whether the year-endbonuses paid by Jones & Ryan were different from the population mean.b. Suppose a sample of 40 Jones & Ryan employees showed a sample mean year-endbonus of $118,000. Assume a population standard deviation of _ _ $30,000 and computethe p-value.c. With ? _ .05 as the level of significance, what is your conclusion?d. Repeat the preceding hypothesis test using the critical value approach.5.Fowle Marketing Research, Inc., bases charges to a client on the assumption that telephonesurveys can be completed in a mean time of 15 minutes or less. If a longer mean surveytime is necessary, a premium rate is charged. A sample of 35 surveys provided the surveytimes shown in the website file named Fowle. Based upon past studies, the population standarddeviation is assumed known with ? _ 4 minutes. Is the premium rate justified?a. Formulate the null and alternative hypotheses for this application.b. Compute the value of the test statistic.c. What is the p-value?d. At ? _ .01, what is your conclusion?
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