You wish to test the following claim (HaHa) at a significance level of =0.005=0.

Question

You wish to test the following claim (HaHa) at a significance level of =0.005=0.005.

      Ho:1=2Ho:1=2
      Ha:12Ha:12

You obtain the following two samples of data.

Sample #1 Sample #2 54.8 47.9 58.9 71.3 68.2 35.5 57.6 54.4 55.1 46.7 47.9 62.1 58.9 52 58.9 31.3 58.7 63.7 52.4 49.5 52.4 49.2 65.6 57.6 49.7 58.4 59.5 52 38.6 47.3 51.2 37.8 55.8 50 43.6 60.7 47.4 42 50.9 52.6 51.9 51.2 54.7 43.4 63.7 44.1 50.1 42.9 48.7 63.7 52.9 46.2 51 41.7 50.6 47.9 50.4 56.9 57.2 42.9 50.2 50.4 38.4 53.1 49.3 50.4 42.6 53.5 49.9 34.9 42.6 57.2 57.6 52.9 48.7

Explanation / Answer

H0: 1 - 2 = 0 i.e. (1 = 2)

H1: 1 - 2 0 i.e. (1 2)

            

Assuming population variances are equal, we would have to calculate pooled-variance t-Test keeping Sample 1 as population 1 and Sample 2 as population 2: -

Sp^2 = (n1-1)S1^2+(n2-1)S2^2/(n1-1)+(n2-1)

         = (36-1)*8.83^2+(39-1)*6.217^2/35+38

         = 2728.58+1468.834/73

         = 57.5

tSTAT=(X1-X2)-(µ1-µ2)/Sp^2(1/n1+1/n2)

       =(53.2-49.66)-0/57.5(1/36+1/39)

       =3.54/1.7525

       =2.02

The P-Value is .047054

Sample 1 Sample 2 54.8 47.4 68.2 51.9 55.1 63.7 58.9 48.7 58.7 51 52.4 50.4 49.7 50.2 38.6 49.3 55.8 49.9 47.9 57.6 35.5 42 46.7 51.2 52 44.1 63.7 63.7 49.2 41.7 58.4 56.9 47.3 50.4 50 50.4 58.9 34.9 57.6 52.9 47.9 50.9 58.9 54.7 52.4 50.1 65.6 52.9 59.5 50.6 51.2 57.2 43.6 38.4 71.3 42.6 54.4 42.6 62.1 48.7 31.3 52.6 49.5 43.4 57.6 42.9 52 46.2 37.8 47.9 60.7 42.9 53.1 53.5 57.2 53.2 49.65897436 Mean 8.829463663 6.217196777 Std Dev 36 39 n

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