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Tests of means and proportions and Tests of variances

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TESTS OF MEANS AND PROPORTIONS
9.52 At Ajax Spring Water, a half-liter bottle of soft drink is supposed to contain a mean of 520 ml. The filling process follows a normal distribution with a known process standard deviation of 4 ml. (a) Which sampling distribution would you use if random samples of 10 bottles are to be weighed? Why? (b) Set up hypotheses and a two-tailed decision rule for the correct mean using the 5 percent level of significance. (c) If a sample of 16 bottles shows a mean fill of 515 ml, does this contradict the hypothesis that the true mean is 520 ml?

TESTS OF MEANS AND PROPORTIONS
9.56 A coin was flipped 60 times and came up heads 38 times. (a) At the .10 level of significance, is the coin biased toward heads? Show your decision rule and calculations. (b) Calculate a p-value and interpret it.

TESTS OF MEANS AND PROPORTIONS
9.60 Ages for the 2005 Boston Red Sox pitchers are shown below. (a) Assuming this is a random sample of major league pitchers, at the 5 percent level of significance does this sample show that the true mean age of all American League pitchers is over 30 years? State your hypotheses and decision rule and show all work. (b) If there is a difference, is it important? (c) Find the p-value and interpret it. (Data are from http://www.boston.redsox.mlb.com.) RedSox
Ages of Boston Red Sox Pitchers, October 2005
Arroyo 28 Foulke 33 Mantei 32 Timlin 39
Clement 31 Gonzalez 30 Miller 29 Wakefield 39
Embree 35 Halama 33 Myers 36 Wells 42

TESTS OF VARIANCES
9.78 * Is this sample of 25 exam scores inconsistent with the hypothesis that the true variance is 64 (i.e., σ = 8)? Use the 5 percent level of significance in a two-sided test. Show all steps, including the hypotheses and critical values from Appendix E. Exams
80 79 69 71 74
73 77 75 65 52
81 84 84 79 70
78 62 77 68 77
88 70 75 85 84

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