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You asked: "Fowle Marketing Research, Inc., bases...

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You asked: "Fowle Marketing Research, Inc., bases charges to a client on the assumption that telephone surveys can be completed in a mean time of 15 minutes or less. If a longer mean survey time is necessary, a premium rate is charged. Suppose a sample of 35 surveys shows a sample mean of 17 minutes. Use = 4 minutes. Is the premium rate justified? a. Formulate the null and alternative hypotheses for this application. H0: Ha: b. Compute the value of the test statistic (to 2 decimals). c. What is the p-value (to 4 decimals)? d. Using = .01, is a premium rate justified for this client? Nielsen reported that young men in the United States watch 56.2 minutes of prime-time TV daily (The Wall Street Journal Europe, November 18, 2003). A researcher believes that young men in Germany spend more time watching prime-time TV. A sample of German young men will be selected by the researcher and the time they spend watching TV in one day will be recorded. The sample results will be used to test the following null and alternative hypotheses. H0: less than or equal to 56.2 Ha: greater than 56.2 a. In this situation, a Type I error would occur if it was concluded that the population mean prime-time TV viewing for young men in Germany was minutes per day when in fact it was not. b. In this situation, a Type II error would occur if it was concluded that the population mean prime-time TV viewing for young men in Germany was minutes per day when in fact it was not The Employment and Training Administration reported the U.S. mean unemployment insurance benefit of $238 per week (The World Almanac 2003). A researcher in the state of Virginia anticipated that sample data would show evidence that the mean weekly unemployment insurance benefit in Virginia was below the national level. a. Develop appropriate hypotheses such that rejection of H0 will support the researcher's contention. H0: Ha: b. For a sample of 110 individuals, the sample mean weekly unemployment insurance benefit was $231 with a sample standard deviation of $90. The p-value is c. Using = .05, can you conclude that the mean weekly unemployment insurance benefit in Virginia is below the national level? Answer the next three questions using the critical value approach. d. Using = .05, what is the critical value for the test statistic (to 2 decimals)? e. State the rejection rule: Reject H0 if t is the critical value. f. Using = .05, can you conclude that the mean weekly unemployment insurance benefit in Virginia is below the national level? Raftelis Financial Consulting reported that the mean quarterly water bill in the United States is $47.50 (U.S. News && World Report, August 12, 2002). Some water systems are operated by public utilities, whereas other water systems are operated by private companies. An economist pointed out that privatization does not equal competition and that monopoly powers provided to public utilities are now being transferred to private companies. The concern is that consumers end up paying higher-than-average rates for water provided by private companies. The water system for Atlanta, Georgia, is provided by a private company. A sample of 64 Atlanta consumers showed a mean quarterly water bill of $51 with a sample standard deviation of $12. At = .05, does the Atlanta sample support the conclusion that above-average rates exist for this private water system? a. State your hypotheses. H0: Ha: b. What is the t statistic (to 2 decimals)? c. The p-value is d. Can you conclude that above-average rates exist for this private water system? The manager of the Danvers-Hilton Resort Hotel stated that the mean guest bill for a weekend is $600 or less. A member of the hotel's accounting staff noticed that the total charges for guest bills have been increasing in recent months. The accountant will use a sample of weekend guest bills to test the manager's claim. a. Which form of the hypotheses should be used to test the manager's claim? H0: Ha: b. When H0 cannot be rejected, can we conclude that the manager's claim is wrong? c. When H0 can be rejected, can we conclude that the manager's claim is wrong? Speaking to a group of analysts in January 2006, a brokerage firm executive claimed that at least 70% of investors are currently confident of meeting their investment objectives. A UBS Investor Optimism Survey, conducted over the period January 2 to January 15, found that 67% of investors were confident of meeting their investment objectives (CNBC, January 20, 2006). a. Formulate the hypotheses that can be used to test the validity of the brokerage firm executive's claim. H0: p Ha: p b. Assume the UBS Investor Optimism Survey collected information from 300 investors. What is the p-value for the hypothesis test (to 4 decimals)? c. At = .05, should the executive's claim be rejected? Consider the following hypothesis test: H0: 12 Ha: > 12 A sample of 25 provided a sample mean = 14 and a sample standard deviation s = 4.32. a. Compute the value of the test statistic (to 2 decimals). b. Use the t distribution table (Table 2 in Appendix B) to compute a range for the p-value. The p-value is Answer the next three questions using the critical value approach. c. Using = .05, what is the critical value for the test statistic? d. State the rejection rule: Reject H0 if t is the critical value. e. Using = .05, can you conclude that the population mean is greater than 12? Wall Street securities firms paid out record year-end bonuses of $125,500 per employee for 2005 (Fortune, February 6, 2006). Suppose we would like to take a sample of employees at the Jones & Ryan securities firm to see whether the mean year-end bonus is different 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-end bonuses paid by Jones & Ryan were different from the population mean. H0: Ha: b. Suppose a sample of 40 Jones & Ryan employees showed a sample mean year-end bonus of $118,000. Assume a population standard deviation of $35,000 and compute the p-value (to 4 decimals). c. With = .05 as the level of significance, what is your conclusion? Answer the next three questions using the critical value approach. d. Using = .05, what is the critical value for the test statistic? +/- e. Calculate the test statistic (to 2 decimals). f. Using = .05, can you conclude that the year-end bonuses paid by Jones & Ryan were different from the population mean? A study found that, in 2005, 12.5% of U.S. workers belonged to unions (The Wall Street Journal, January 21, 2006). Suppose a sample of 390 U.S. workers is collected in 2006 to determine whether union efforts to organize have increased union membership. a. Formulate the hypotheses that can be used to determine whether union membership increased in 2006. H0: p Ha: p b. If the sample results show that 50 of the workers belonged to unions, what is the sample proportion of workers belonging to unions (to 2 decimals)? c. Complete the following, assuming an level of .05. Compute the value of the test statistic (to 2 decimals). What is the p-value (to 4 decimals)? What is your conclusion?

 

Paper#8302 | Written in 18-Jul-2015

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