Question

Are my answers correct?

2. Gravetter/Wallnau/Forzano, Essentials - Chapter 10 - End-of-chapter question 6 Two separate samples receive different treatments. After treatment, the first sample has n = 6 with SS = 236, and the second has n = 12 with SS = 340. The pooled variance for the two samples is 36.00 . Compute the estimated standard error for the sample mean difference. Estimated S(M1 - M2) = 3.00 If the sample mean difference is 7 points, is this enough to reject the null hypothesis and conclude that there is a significant difference for a two-tailed test at the .05 level? t-critical = = 2.120 2.33 • Reject the null hypothesis; there is a significant difference. Fail to reject the null hypothesis; there is no significant difference. Fail to reject the null hypothesis; there is a significant difference. Reject the null hypothesis; there is no significant difference.

Answer 1

Pooled variance Sp^2 = (SS1+SS2)/(df1+df2) = (236+340)/(5+11) = 36

Sp = 6

Estimatd standard error = Sp * SQRT((1/n1 + 1/n2)) = 6*SQRT(1/6+1/12) = 3

Mean diff = 7

t critical = 2.1199 = 2.120

t stat = (X1 bar-X2 bar )/SQRT(Sp^2*(1/n1 + 1/n2)) = (X1 bar-X2 bar )/SE = 7/3 = 2.33

t stat > t critical, reject H0

Reject H0, there is a significant difference