The weights of 300 adult men were estimated and employed to test the hypothesis that the weights were normally distributed with mean of 160 lb and standard deviation of 15 lb. The data were grouped in the following classes:
Weight (x) Observed Frequency
x < 130 7
130 ≤ x < 145 38
145 ≤ x < 160 100
160 ≤ x < 175 102
175 ≤ x < 190 40
190 ≤ x 13
From the normal table, the percentages for classes are 2.28%, 13.59%, 34.13%, 34.13%, 13.59%, and 2.28%, respectively. Do the observed frequency data give significant reason to discredit the hypothesis that the weights are normally distributed with mean of 160 lb and a standard deviation of 15 lb? Employ α = 0.05.