Question

Based on clothing in museums, the mean height of adult males 100 years ago is believed to be 67 inches. A random sample of 33 currently living adult males has an average height of 68.5 inches and a standard deviation of 5.8 inches. Using alpha = 0.01, determine whether the height of adult males is different than what it used to be.

            9a.) What is the test statistic?

            9b.) What is the critical value?

            9c.) What is your decision?

Answer 1

a) The test statistic t = ()/()

                                 = (68.5 - 67)/(5.8/sqrt(33))

                                 = 1.49

b) DF = 33 - 1 = 32

With 32 df and alpha = 0.01, the critical values are t_{0.005, 32} = +/- 2.738

c) As the test statistic value is not greater than the upper critical value (1.49 < 2.738), so the null hypothesis is not rejected.

At alpha = 0.01, there is not sufficient evidence to conclude that the heights of adults males is different than what it used to be