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MATH 117 Name___________________ Bennett May 4, 2020 Test 4 Form A 1. Set up Ho, Ha, and tell which test and why. Do not complete the test. (10 points) How big are tomatoes? Some say that depends on the growing conditions. A random sample of n1 =89 organically grown tomatoes had a sample mean weight of ounces. Another random sample of n2 = 75 tomatoes that were not organically grown had a sample mean weight of ounces. Previous studies show that ounce and ounces. Does this indicate a difference either way between population mean weights of organically grown tomatoes compared to those that are not organically grown? 2. Set up Ho, Ha, and tell which test and why. Do not complete the test. (10 points) How old are college students? The national distribution for college students is shown below. Age Under 26 26-35 36-45 46-55 Over 55 Number of students 39% 25% 16% 12% 8% The Western Association of Mountain Colleges took a random sample of 212 students and obtained the following sampling distribution. Age Under 26 26-35 36-45 46-55 Over 55 Number of students 65 73 41 21 12 Is the sample age distribution for the Western Association of Mountain Colleges a good fit to the national distribution? 3. Complete the hypothesis test A system specialist has studied work-flow of clerks all doing the same inventory work. Based on this study, she designed a new work-flow layout for the inventory system. To compare average production for the old and new methods, a random sample of 6 clerks was used. The average production rate (number of inventory items processed per shift) for each clerk was measured before and after the new system was introduced. The results are shown below. Test the claim that the new system increases the mean number of items processed per shift. Use α = .05. (20 points) Clerk 1 2 3 4 5 6 B: Old 116 108 93 88 119 111 A: New 123 114 112 82 127 122 4. Complete the hypothesis test Are teacher evaluations independent of grades? After midterm, a random sample of 284 students was asked to evaluate teacher performance. The students were asked to supply their midterm grade in the course being evaluated. In this study, only students with passing grades (A, B, or C) were included in the summary table. Use the 5% significance level to test the claim that teacher evaluations are independent of midterm grades. (20 points) Midterm grade Teacher evaluation A B C Row total Positive 35 33 28 96 Neutral 25 46 35 106 Negative 20 22 40 82 Column total 80 101 103 284 5. Complete the hypothesis test This problem is based on information taken from Life in America’s Fifty States, by G. S. Thomas. A random sample of 153 people ages 16 to 19 were taken from the island of Oahu, Hawaii, and 12 were found to be high school dropouts. Another random sample of 128 people ages 16 to 19 were taken from Sweetwater, Wyoming, and 7 were found to be high school dropouts. Do these data indicate that the population proportion of high school dropouts on Oahu is different from that of Sweetwater County? (20 points) 6. Complete the hypothesis test High levels of cholesterol in the blood are not healthy in either humans or dogs. Because a diet rich in saturated fats raises the cholesterol level, it is plausible that dogs owned as pets have higher cholesterol levels than dogs owned by a veterinary research clinic. “Normal levels of cholesterol based on the clinic’s dogs would be misleading. A clinic compared healthy dogs it owned with healthy pets brought to the clinic to be neutered. The summary statistics for blood cholesterol levels (milligrams per deciliter of blood) appear below. Is this good evidence that there is a difference between the clinic dogs and the dogs owned as pets? (20 points) Group N Mean Standard deviation Pets 26 193 68 Clinic 23 174 44
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