ime261a10s - Problem9.26 Paired T-Test and CI Two days...

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Assignment 10 Solutions Problem 9.26 Paired T-Test and CI: Two days, Seven days Paired T for Two days - Seven days N Mean StDev SE Mean Two days 40 2.9910 0.4961 0.0784 Seven days 40 3.5441 0.5036 0.0796 Difference 40 -0.5531 0.3733 0.0590 99% upper bound for mean difference: -0.4100 T-Test of mean difference = 0 (vs < 0): T-Value = -9.37 P-Value = 0.000 a) H o : μ 2 > μ 7 H 1 : μ 2 7 α = 0.01 n=40 Samples are not independent Î Paired Test D bar = 0.5531 S D =0.3733 t o = ି଴.ହହଷଵି଴ బ.యళయయ √రబ ൌ െ9.37 t 0.01, 39 = 2.4258 Î 2.4258 (because area shaded below this value must be equal to α =0.01) Reject H o , At a 1% significance level there is enough information to conclude the mean strength is less at 2 days than at 7 days. b) It is necessary to assume that the differences between observations are normally distributed. c) P value = 0.000 (from Minitab) or P value <0.005 (from table). This is the probability of obtaining a test statistic value less than the result obtained from the sample data if H 0 were true.