Show all work. No work = no credit. 1. A medical researcher conjectures that smoking can result in wrinkled skin around the eyes. The researcher recruited 150 smokers and 250 nonsmokers to take part in an observational study and found that 95 of the smokers and 105 of the nonsmokers were seen to have prominent wrinkles around the eyes (based on a standardized wrinkle score administered by a person who did not know if the subject smoked or not). a. Of the 150 smokers, 95 had prominent wrinkles around the eyes. Construct a 95% confidence interval for the proportion of smokers who have prominent wrinkles around the eyes. Show the work in computing the bounds of the interval. (12 pts.) Round to 3 decimal places. df=n-^=1-1=149 -2=0.95 2=0.05 = 0.025 22/2 Unorm=(0,025,0,1) = -1.95 0.025 b. Use a complete sentence to interpret the result of part (a). (3 pts.) are 95% confidente that the confidence interva proportion Smakers who have promement be around the eyes is betwam f and c. Of the 250 nonsmokers, 105 had prominent wrinkles around the eyes. Construct a 95% confidence interval for the proportion of nonsmokers who have prominent wrinkles around the eyes. Show the work in computing the bounds of the interval. (12 pts.) Round to 3 decimal places. MAT 152, Estimation Lab Name d. Use a complete sentence to interpret the result of part (c). (3 pts.) e. Based on the results from above, do these data provide evidence that smokers have a significantly higher rate of prominent wrinkles than nonsmokers? Explain. (4 pts.) 2. The lifetimes of calculator batteries is being investigated by Consumer Digest. They find that the average life of 45 Everset batteries is 125.245 hours and the standard deviation is 34.890 hours. For JordoVac the average life of 50 batteries is 120.051 hours and the standard deviation is 42.801 hours. a. Construct a 99% confidence interval for the mean life of Everset batteries. Show all work. Round to 3 decimal places. (10 pts.) b. Use a complete sentence to interpret the result of part (a). (3 pts.) T MAT 152, Estim C. Construct a 99% confidence interval for the mean life of JordoVac batteries. (10 pts.) Show all work. Round to 3 decimal places. d. Use a complete sentence to interpret the result of part (c). (3 pts.) e. Can you conclude based on these data that there is a difference in the mean life of Everset and JordoVac batteries? Explain, using the results from above. (4 pts.) 3. A marketing research consultant hired by an ice cream manufacturer is interested in determining the proportion of customers who will purchase its new flavor of ice cream. How many people would have to be surveyed to be 90% confident that you can estimate the proportion of people who favor Coca-Cola within 1.5 percentage points: a. If no prior estimate of the proportion is known? (6 pts.) b. If a pilot study finds a proportion of 20% that would purchase the new flavor? (6 pts.) 118.3 5.7 16 0.98 4. a. A random sample of 16 Americans yielded the following data on the number of pounds of beef consumed per year: 118 115 125 110 112 130 117 112 115 120 113 118 119 122 123 126 What is the average number of pounds of beef consumed each year per person in the United States? Assume that the distribution of pounds of beef consumption per year is normally distributed. Compute the sample mean and sample standard deviation. Round to one decimal place. (4 pts.) X=118.3 Sx=5.7 n=16 b. Construct a 98% confidence interval using the sample data. Show one decimal place in the bounds of the confidence interval. Show all work in computing the margin of error and the bounds. (10 pts.) 1-9=0.97 =0.02 =2/2 =0.01 In-1=15 inut = (0.98,15) +4 = 0.01 t=0,02 =2.249 E=2.249 | JTS 5. A team of researchers wants to estimate the mean IQ of students enrolled at one prestigious university. Previous research studies have examined samples of students from other similar universities and usually find results with s=10. In order to construct a 99% confidence interval with a margin of error of +2 IQ points, what sample size should be obtained? (10 pts.)