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Spring 2008 Math 227 Test #3 (ch 7, 8 & 9) Name: ____________________ Show all necessary work for full credit. Total: 100 points. 1. (10 points) Suppose that the weight of the cereal in boxes of Loopy Froots breakfast cereal is normally distributed. A consumer advocate group randomly sampled 8 boxes of Loopy Froots and weighed the contents (in grams): 535, 540, 565, 575, 535, 558, 564, and 550. a. Find the sample mean and sample standard deviation. b. Construct a 95% confidence interval for the mean average of the weight of the cereal in boxes of Loop Froots. 2. (10 points)A marketing research is conducting a survey to determine what proportion of consumers between the ages of 18 and 35 own an iPod. Sixty individuals in that age range were randomly sampled and 11 of them own iPod. a. Find a point estimate for the proportion of consumers who own iPod. b. Construct a 90% confidence interval for p 3. (10 points)Assume that the previous Test scores were normally distributed. For a random sample of size 5, the scores were 72, 48, 65, 59 and 37. a. Find the sample mean, and the sample standard deviation b. Construct the 95%-confidence interval for standard deviation of the previous Test scores. 4. (10 points)A market researcher for a consumer electronics company wants to study the weekly TV viewing habits of residents of a particular city. A random sample of 41 respondents is selected and the sample resulted a mean of 15.3 hours with 3.8 hours standard deviation. Assume that the amount of time of TV viewing per week is normally distributed. Test the claim at 5% significant level that the mean of viewing habit is more than 14 hours per week. 5. (8 points)The Wechsler IQ test is designed so that the mean is 100 and the standard deviation is 15 for the population of normal adults. Find the sample size necessary to estimate the mean IQ score of statistics students. We want to be 95% confident that our sample mean is within 2 IQ points of the true mean. Assume 15 . 6. (12 points) Eight different families are tested for the number of gallons of water a day they use before and after viewing a conservation video. At the 0.01 significance level, test the claim that the mean is the same before and after the viewing. Assume the sample is drawn from normal population. Before 34 33 38 33 40 31 33 35 After 33 28 25 35 31 28 35 28 7. (10 points)A section of Highway 405 in Los Angeles has a speed limit of 65 mi/h, and recorded speeds are listed below for randomly selected cars traveling on northbound and southbound lanes. Highway 405 North: 68 68 72 73 65 74 73 72 68 65 65 73 66 71 68 74 66 71 65 73 Highway 405 South: 59 75 70 56 66 75 68 75 62 72 60 73 61 75 58 74 60 73 58 75 Assume that the speeds are from normally distributed population; test the claim that the mean speed on the northbound lanes is equal to the mean speed on the southbound lanes. Use 0.01 8. (10 points)In a study of store checkout scanners, 1234 items were checked and 20 checked items were found to be overcharges, and 1214 checked items were not overcharges. Use a 0.05 significance level to test the claim that with scanners, 1% of sales are overcharges. 9. (10 points)A survey of 436 workers showed that 192 of them said that it was seriously unethical to monitor employee e-mail. When 121 senior-level bosses were surveyed, 40 said that it was seriously unethical to monitor employee e-mail. Construct a 90% confidence interval estimate of the difference between the two population proportions. Is there a substantial gap between the employees and bosses? 10. (10 points)Use a 0.05 significance level to test the claim that heights of female supermodels vary less than the heights of women in general. The standard deviation of heights of the population of women is 2.5 in. Listed below are the heights (in inches) of randomly selected supermodels. Assume that the heights are from normally distributed population. 71 71 70 69 69.5 70.5 71 72 70 70 69 69.5 69 70 70 66.5 70 71