1. Mars Inc. claims that they produce M&Ms with the following distributions: 20% 25% Yellow 25% Red Orange Green 15% 10% 5% Blue Brown A bag of M&Ms was randomly selected from the grocery store shelf, and the color counts were: 26 23 Yellow 22 Red Orange 14 Green 16 13 Blue Brown Using the 2 goodness of fit test ( = 0.05) to determine if the proportion of M&Ms is what is claimed. Select the [test statistic, p value, Decision to Reject (RH0) or Failure to Reject (FRH0)]. a) [2 = 15.374, pvalue = 0.009, RH0] b) [2 = 15.374, pvalue = 0.009, FRH0] c) [2 = 15.374, pvalue = 0.004, RH0] d) [2 = 7.687, pvalue = 0.991, FRH0] e) [2 = 7.687, pvalue = 0.991, RH0] f) None of the above 2. Solid fats are more likely to raise blood cholesterol levels than liquid fats. Suppose a nutritionist analyzed the percentage of saturated fat for a sample of 6 brands of stick margarine (solid fat) and for a sample of 6 brands of liquid margarine and obtained the following results: We want to determine if there a significant difference in the average amount of saturated fat in solid and liquid fats. What is the test statistic? (assume the population data is normally distributed) a) z = 37.765 b) z = 37.265 c) t = 37.265 d) t = 37.765 e) t = 24.951 3. In a experiment on relaxation techniques, subject's brain signals were measured before and after the relaxation exercises with the following results: Person 1 2 3 4 5 Before 31 37 66 52 28 26 34 58 51 26 After Assuming the population is normally distributed, is there sufficient evidence to suggest that the relaxation exercise slowed the brain waves? (Use =0.05) a) Fail to reject the null hypothesis which states there is no change in brain waves. b) Reject the null hypothesis which states there is no change in brain waves in favor of the alternate which states the brain waves slowed after relaxation. c) There is not enough information to make a conclusion. 4. An experimenter flips a coin 100 times and gets 62 heads. Test the claim that the coin is fair against the twosided claim that it is not fair at the level =.01. a) Ho: p = .5, Ha: p .5; z = 2.40; Reject Ho at the 1% significance level. b) Ho: p = .5, Ha: p .5; z = 2.47; Fail to reject Ho at the 1% significance level. c) Ho: p = .5, Ha: p > .5; z = 2.40; Reject Ho at the 1% significance level. d) Ho: p = .5, Ha: p > .5; z = 2.47; Fail to reject Ho at the 1% significance level. e) Ho: p = .5, Ha: p .5; z = 2.40; Fail to reject Ho at the 1% significance level. 5. It is believed that the average amount of money spent per U.S. household per week on food is about $97, with standard deviation $12. A random sample of 25 households in a certain affluent community yields a mean weekly food budget of $100. We want to test the hypothesis that the mean weekly food budget for all households in this community is higher than the national average. State the null and alternative hypotheses for this test, the test statistic and determine if the results significant at the 5% level. a) Ho: = 97, Ha: > 97; z = 1.250; Yes, we should reject Ho. b) Ho: = 97, Ha: 97; z = 0.125; No, we should fail to reject Ho. c) Ho: = 97, Ha: < 97; z = 0.125; Yes, we should reject Ho. d) Ho: = 97, Ha: > 97; z = 1.250; No, we should fail to reject Ho. e) Ho: = 97, Ha: 97; z = 1.250; No, we should fail to reject Ho. 6. An auditor for a hardware store chain wished to compare the efficiency of two different auditing techniques. To do this he selected a sample of nine store accounts and applied auditing techniques A and B to each of the nine accounts selected. The number of errors found in each of techniques A and B is listed in the table below: Errors in A 45 48 46 48 52 50 49 40 45 Errors in B 31 37 39 37 54 45 49 41 50 Select a 90% confidence interval for the true mean difference in the two techniques. a) [3.050, 5.838] b) [4.183, 4.183] c) [2.584, 6.304] d) [2.195, 6.693] e) [0.261, 8.627] f) None of the above 7. An oil company is interested in estimating the true proportion of female truck drivers based in five southern states. A statistician hired by the oil company must determine the sample size needed in order to make the estimate accurate to within 1% of the true proportion with 97% confidence. What is the minimum number of truck drivers that the statistician should sample in these southern states in order to achieve the desired accuracy? a) 11756 b) 11794 c) 11757 d) 11773 e) 11787 f) None of the above 8. The gas mileage for a certain model of car is known to have a standard deviation of 5 mi/gallon. A simple random sample of 100 cars of this model is chosen and found to have a mean gas mileage of 26.5 mi/gallon. Construct a 98% confidence interval for the mean gas mileage for this car model. a) [25.473, 27.527] b) [14.870, 38.130] c) [25.337, 27.663] d) [26.384, 26.616] e) [16.230, 36.770] f) None of the above