A twosample ttest is going to be carried out where it is ass

A two-sample t-test is going to be carried out where it is assumed that the population variances are unknown but assumed equal. The first sample of 30 items were chosen and measured. For this first sample, an average response of 125 with a sample variance of 25 was found. The second sample of 40 items were chosen and measured. This second sample had an average response of 132 with a sample variance of 16. What is the pooled standard deviation for this problem? (rounded to second place after the decimal)

Solution

Sample 1 size 30
Sample 2 size 40
Sample 1 mean 125
Sample 2 mean 132
Sample 1 S.D. 5
Sample 2 S.D. 4
Pooled S.D = [(n1-1)s1^2+(n2-1)s2^2]/(n1+n2-2)
Pooled variance s = [(29)(25)+(39)(16))] / (68) =
Pooled variance s^2 = 19.838235
=19.84