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CHAPTER 9HYPOTHESIS TESTS PROBLEM 1. The Department of Economic and Community Development (DECD) reported that in 2005 the aver age number of new...

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CHAPTER 9—HYPOTHESIS TESTS PROBLEM 1. The Department of Economic and Community Development (DECD) reported that in 2005 the aver- age number of new jobs created per county was 450. The department also provided the following in- formation regarding a sample of 5 counties in 2006. County New Jobs Created In 2006 Bradley 410 Rhea 480 Marion 407 Grundy 428 Sequatchie 400 a. Compute the sample average and the standard deviation for 2006. b. We want to determine whether there has been a significant decrease in the average number of jobs created. Provide the null and the alternative hypotheses. c. Compute the test statistic. d. Compute the p -value; and at 95% confidence, test the hypotheses. Assume the population is normally distributed. 2. The Bureau of Labor Statistics reported that the average yearly income of dentists in the year 2005 was $110,000. A sample of 81 dentists, which was taken in 2006, showed an average yearly income of $120,000. Assume the standard deviation of the population of dentists in 2006 is $36,000. a. We want to test to determine if there has been a significant increase in the average yearly in- come of dentists. Provide the null and the alternative hypotheses. b. Compute the test statistic. c. Determine the p -value; and at 95% confidence, test the hypotheses. 3. A producer of various kinds of batteries has been producing "D" size batteries with a life expectancy of 87 hours. Due to an improved production process, management believes that there has been an in- crease in the life expectancy of their "D" size batteries. A sample of 36 batteries showed an average life of 88.5 hours. Assume from past information that it is known that the standard deviation of the population is 9 hours. a. At 99% confidence using the critical value approach, test management's belief. b. What is the p -value associated with the sample results? What is your conclusion based on the p -value? 4. A new soft drink is being market tested. A sample of 400 individuals participated in the taste test and 100 indicated that they like the taste. We are interested in determining if more than 21% of the popula- tion will like the new soft drink. a. Set up the null and the alternative hypotheses. b. Determine the test statistic.
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c. Determine the p -value. d. At 95% confidence, test to determine if more than 21% of the population will like the new soft drink. 5. An official of a large national union claims that the fraction of women in the union is not significantly different from one-half. Using the critical value approach and the sample information reported below, carry out a test of this statement. Let α = 0.05. sample size 400 women 168 men 232
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1.A population of 1,000 students spends an average of $10.50 a day on dinner. The standard deviation
of the expenditure is $3. A simple random sample of 64 students is taken.
a. What are the...

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