Various quantities related to performance

1. Computers in some vehicles calculate various quantities related to performance. One of these is the fuel efficiency, or gas mileage, usually expressed as miles per gallon (mpg). For one vehicle equipped in this way, the mpg were recorded each time the gas tank was filled, and the computer was then reset.13 Here are the mpg values for a random sample of 20 of these records: Suppose that the standard deviation is known to be s = 3.5 mpg. Assume the distribution is normal and construct a 99% confidence interval for µ, the mean mpg for this vehicle. 2. Since previous studies have reported that elite athletes are often deficient in their nutritional intake (e.g., total calories, carbohydrates, protein), a group of researchers decided to evaluate Canadian high performance athletes. A total of n = 324 athletes from eight Canadian sports centers participated in the study. One reported finding was that the average caloric intake among the n = 201 women was 2403.7 kcal/day. The recommended amount is 2811.5 kcal/day. Is there evidence that female Canadian athletes are deficient in the caloric intake? Conduct a full hypothesis test for each question. Use ? = 0.05. Go through each of the following steps for each problem. a. State the null and alternative hypotheses. b. State the significance level for this problem. c. Assuming a standard deviation of 880 kcal/day, calculate the test statistic. (Please explain what allowed you to use the particular distribution you choose before calculating your test statistic. Then, write out the correct formula and show your work.) d. State the P-value. e. State whether you reject or do not reject the null hypothesis and give a reason why. f. State your conclusion in context of the problem (i.e. interpret your results by answering the question posed). 3. In addition to the computer computing mpg, the driver also recorded the mpg by dividing the miles driven by the number of gallons at each fill-up. The following data are the differences between the computer’s and the driver’s calculations for that random sample of 20 records. The driver wants to determine if these calculations are different. Assume the standard deviation of a difference to be s = 3.0 4. Conduct a full hypothesis test for each question. Use ? = 0.05. Go through each of the following steps for each problem. a. State the null and alternative hypotheses. b. State the significance level for this problem. c. Calculate the test statistic. (Please explain what allowed you to use the particular distribution you choose before calculating your test statistic. Then, write out the correct formula and show your work.) d. State the P-value. e. State whether you reject or do not reject the null hypothesis and give a reason why. f. State your conclusion in context of the problem (i.e. interpret your results by answering the question posed).

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