Course Notes - Department of Mathematics and Statistics

Find the p-value:Pr(Z < -2.78)=0.0027• Can get p-value directly from Rcmdr.• Use pnorm(-2.78).• If p-value < 0.05 we have significance at the 5% level (and ifp-value < 0.01 we have significance at the 1% level).Make the conclusion:Very small amount of support for H 0 (p-value is less than 0.05).The observation is a rare event. Reject H 0 and accept H A .There is evidence that after the education campaign the proportionbecoming pregnant has reduced.7.3 Hypothesis Test Difference Two MeansEXAMPLE THREE - HYPOTHESIS TEST FOR THE DIFFERENCE BETWEENTWO MEANSThe height of an adult is thought to be associated with sex (male orfemale). From the questionnaire in week one, the means and variancesof the heights of males and females enrolled in STAT110 are below.Female MaleSample mean (x i ) 166.6 180.6Sample standard deviation (s i ) 8.04 7.97Sample size (n i ) 176 133Investigate the claim that the mean heights are different for the twosexes (assume H A is study driven).Set up the hypotheses:STEP ONE: H 0 : µ male − µ female = 0 (the null hypothesis)STEP TWO: H A : µ male − µ female ≠ 0 (the research hypothesis)123