mean 1 = BSMT mean
mean 2 = BSMARE mean
We are going to be performing a two-sample t-test.
The null hypothesis Ho: mean1 - mean 2 = 0
Ha: mean1 - mean 2 != 0
the t-statistic is mean1 - mean 2
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sqrt(s1^2/n1^2 + s2^2/n2^2)
where mean 1 = 83, mean 2 = 85, s1 = 2.75, s2 = 2.65, n1 = 40 and n2 = 55
assuming equal variances, the degrees of freedom is n1 + n2 - 2 = 93, the t-statistic is -3.5747 and the p-value for a two-sided test is 0.0006.
assuming unequal variances, the degrees of freedom is 82, the t-statistic is -3.5537 and the p-value for a two-sided test is 0.0006.
Generally, we would assume unequal variances Either way, since the p-value is < 0.05, the null hypothesis is rejected and there is convincing evidence that there is a difference in the qualifying mean scores at the 0.05 level of significance.
