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    Standard Deviation, Average Number & P-Value Questions

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    1) The club professional at a difficult public course boasts that his course is so tough that the average golfer loses a dozen or more golf balls during a round of golf. A dubious golfer sets out to show that the pro is fibbing. He asks a random sample of 15 golfers who just completed their rounds to report the number of golf balls each lost. Assuming that the number of golf balls lost is normally distributed with a standard deviation of 3, can we infer at the 10% significance level that the average number of golf balls lost is less than 12?
    1 14 8 15 17 10 12 6
    14 21 15 9 11 4 4 8

    2) A random sample of 12 second-year university students enrolled in a business statistics course was drawn. At the course's completion, each student was asked how many hours he or she spent doing homework in statistics. The data are listed here. It is known that the population standard deviation is ? = 8.0. The instructor has recommended that students devote 3 hours per week for the duration of the 12-week semester, for a total of 36 hours. Test to determine whether there is evidence that the average student spent less than the recommended amount of time. Compute the p-value of the test.
    31 40 26 30 36 38 29 40 38 30 35 38

    3) Spam e-mail has become a serious and costly nuisance. An office manager believes that the average amount of time spent by office workers reading and deleting spam exceeds 25 minutes per day. To test this belief, he takes a random sample of 18 workers and measures the amount of time each spends reading and deleting spam. The results are listed here. If the population of times is normal with a standard deviation of 12 minutes, can the manager infer at the 1% significance level that he is correct?
    35 48 29 44 17 21 32 28 34
    23 13 9 11 30 42 37 43 48

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