The University is considering changing the email system that they currently use.

Question

The University is considering changing the email system that they currently use. Since there are substantial learning costs associated with any new software, the University only wants to change to the new system if it is very confident that there is at least a 20% difference in the proportion of faculty and staff who say they like the new system. In a sample of 140 users of the current system, the University finds that 75 say they like the current system. In another sample of 85 experimental users of the “new” system, the University finds that 72 of them like the new system. When testing the hypothesis (using a 5% level of significance) that there is at least a 20% difference in the proportion of users who like the two systems, what is the null and alternative hypothesis? (please write out the null and alternative hypotheses below AND on your scratch work...failure to do BOTH will result in 0 points)

Explanation / Answer

p1=75/140=0.5357, var(p1)=(p1*(1-p1)/n1)=(0.5357*(1-0.5357)/140)=0.001777, SE(p1)=sqrt(0.0018)=0.0421

p2=72/85=0.8471, Var(p2)=(0.8471*(1-0.8471)/85)=0.001524, SE(p2)=sqrt(0.001524)=0.0390

|p1-p2|=absolute(0.5357-0.8471)=0.3114

SE(p1-p2)=sqrt(var(p1)+var(p2))=sqrt(0.001777+0.001524)=0.0575

null hypothesis H0: |p1-p2|<=0.2

althernaty hypothesis H1: |p1-p2|>0.2

we use z-test to test the null hypothessis and z=(|(p1-p2)|-0.2)/SE(p1-p2)=(0.3114-0.2)/0.0575=1.94

one talied z(0.05)=1.6449 is less than calculated z=1.94, so we fail to accept H0 and conclude that difference is more than 0.2 or 20%

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