Question

1. In 1990, the mean height of women 20 years of age or older was 63.7 inches based on data obtained from the CDC. Suppose that a random sample of 45 women who are 20 years of age or older in 2015 results in a mean height of 63.9 inches with a standard deviation of 0.5 inch. Does your sample provide sufficient evidence that women today are taller than in 1990? Perform the appropriate test at the 0.05 level of significance. (a) Give the appropriate hypotheses for this test and define any parameters used. (b) List and verify conditions for the appropriate hypothesis test. (c) Give the appropriate test statistic. Show formula, work, and value. (d) Find the rejection region. Draw an appropriate picture, show work. (e) What is your decision regarding the null hypothesis? (f) What are your conclusions about this particular test?

Answer 1

= 63.7, n=45, X = 63.9 S=0.5, -0.05 (2) Hoi l = 63.1 I Hai lu > 63.7 l - The mean heigh of women 20 years of age or older was 63.7 inches (6) Wind to test for one sample mean o is unknown and Sample is doawn from the population co Test statistic: X- 4 6 3-9-63.7 s/n 0.5 t us It = 2.683 (d) At 2 = 0.00 1.0.5, df = 44 (sight toiled) to critical value = 1.680 1. = 2.6833 rejection Accept (region region V (e) Decision sule: reject Ho if t>1.680 1. GPO f) conclusion: Al 2-0.05 lo.s there is enough evidence to claim that women today are taller than in 1990