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Tests of Significance and Confidence Intervals for Means 1. A random sample of 156 fields of durum wheat has a mean yield of 26.8 bushels per acre and standard deviation of 8 bushels per acre. Find a 95% confidence interval for the mean yield per acre of durum wheat. 2. As part of your study on the food consumption habits of teenage males, you randomly select 20 teenage males and ask each how many 12-ounce servings of soda they drink per day. The results are listed below. Assume an underlying normal distribution. At the 5% significance level, is there enough evidence to claim that teenage males drink less than 3.0 twelve-ounce servings per day? 3.3 2.1 2.5 2.1 3.4 3.3 4.4 3.4 2.5 3.2 2.5 3.8 2.0 2.9 1.9 1.3 1.9 2.8 4.2 2.2 3. A pharmaceutical company claims that its new drug reduces diastolic blood pressure. The diastolic blood pressure (in millimeters of mercury) for 10 patients before taking the new drug and 2 hours after taking the drug is shown in the table below. Assume normal distributions. a. At the 5% significance level, is there enough evidence to support the company's claim? b. Find a 95% confidence interval for the mean difference between the diastolic blood pressure before taking the new drug and 2 hours after taking the drug. Patient 2 3 4 5 6 8 9 10 Before 103 122 106 112 125 98 121 107 105 108 After 98 121 107 105 108 89 102 14 101 108 4. The pathogen Phytophthora capsici causes bell peppers to wilt and die. Because bell peppers are an important commercial crop, this disease has undergone a great deal of agriculture research. Two fields are under study. The first step is to compare the mean soil water content for the two fields. The results are in the table below. Do these data indicate a difference in the soil water content at the 5% significance level? Assume normal population distributions. Field A 10.2 10.7 15.5 10.4 9.9 10.0 16.6 15.1 samples 15.2 13.5 Field B 8.1 8.5 8.4 7.3 8.0 7.1 13.9 12.2 samples 13.4 1 1.3 5. In crash tests at 5 miles per hour, the mean bumper repair cost for 14 randomly selected small cars was $473 with a standard deviation of $190. In similar tests of 23 randomly selected midsize cars, the mean bumper repair cost was $741 with a standard deviation of $205. Assumed that the underlying distributions are normal. At a 10% significance level, should you conclude that the mean bumper repair cost is less for small cars than it is for midsize cars