Answers to Hypothesis Testing Word 2003

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Hypothesis Testing 1. Childhood participation in sports improves self-esteem. A sample of 100 adolescents with a history of group participation is given a self-esteem questionnaire and score a mean of 44. The general population of adolescents scores a mean of 40 with a standard deviation of 12. Does the sample provide evidence that sports participation improves self-esteem. Use a two tailed test at alpha = .05. Z-test Hypotheses: Null: Childhood participation in sports does not improve self-esteem. Alternative: Childhood participation in sports does improve self-esteem. Critical Value: α = .05, two-tailed test, critical value z = ± 1.96 Calculate Your Statistic: n = 100, x = 44, μ = 40, σ = 12 z = (44-40) / (12/√100) = 4/1.2 = 3.33 Conclusion: Reject the null hypothesis. The study shows that adolescents with a history of group participation have significantly different self-esteem than the general population of adolescents. This problem has been slightly changed! 2. Do husbands watch more television than wives? A sample of 20 husbands and 20 wives kept track of their television watching for a two week period. At the end of two weeks the number of hours watched by husbands was compared to the number of hours watched by wives. Wives watched an average of 3.4 more hours than husbands with a standard error of the difference of 1.5 hours. Test for mean differences using a .01 alpha level and two tails. t -test statistic (related samples) Hypotheses: Null: There is no difference in the amount of tv watched by husbands and wives. Alternative: There is a difference in the amount of tv watched by husbands and wives. Critical Value: α = .01, two-tailed test, df = 19, critical value t = ± 2.861 Calculate Your Statistic: D (with a bar over it) = 3.4, M D = 1.5 t = 3.4 / 1.5 = = 2.27 Conclusion: Fail to reject the null hypothesis. The study shows that husbands and wives do not watch significantly different amounts of television. 3. Some speculate that REM sleep associated with dreaming plays a role in memory and learning. For a sample of n=16 college students (who were currently in an exam period) REM activity monitoring produced a mean of 143. The general population of college students have a mean of 110 and a standard deviation of 50. Do the data support the hypotheses that REM activity during exams is higher than during non-exam periods. Use a one-tailed test at alpha = . 01.

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