Problem 3 1,000,000 people followed Atkin's diet for a month. Thirty women were randomly selected and asked about their increased weights, and the data were recorded in Fweight.csv. Another 40 men were randomly selected and asked about their increased weights, and the data were recorded in Mweight.csv. Research shows that following Atkin's diet can make women and men gain the same average weight. Please check the reliability of the study. The standard deviation for all women in this group was 7.1, and the standard deviation for all men in this group was 5. Ho : HM = HF =5 vs. H1 : HM # HF# 5 Z-test: XM = 7.194587 1 - stats.norm.cdf (5 + 2.194587,5, 5/(40**.5)) + stats.norm.cdf(5 - 2.194587,5, 5/(40**.5)) P = 0.005503942337709939 Because the p-value is extremely close to 0, we must fail to reject the alternative hypothesis (H, ) and it must therefore be true. Problem 4 1,000,000 people followed Atkin's diet for a month. Thirty women were randomly selected and asked about their increased weights, and the data were recorded in Fweight.csv. Another 40 men were randomly selected and asked about their increased weights, and the data were recorded in Mweight.csv. Research shows that following Atkin's diet can make women and men gain the same average weight.. Please check the reliability of the study. HO : UM = UF = 5 vs. H1 : UM # UF #5 T-test: teststat = abs(7.194587 - 5)/(4.511195/(40**.5)) pval = stats.t.cdf(teststat, df=40-1) P = 0.998091653368946 Because the p-value is greater than the usual level of significance, we must fail to reject the null hypothesis (Ho) and it must therefore be true