 Solution

ID: past-exam-of-the-statistics-course-of-the-university-of-oxford/2014/1/c/i/solution

The equal-variance two-sample Student's t-test pools the within-group sums of squares. If

s_{A}^{2}

and

s_{B}^{2}

are the two unbiased sample variances, the required positive square root is

S = \frac{\sum _{i = 1}^{m} ( A _{i} - A ) ^{2} + \sum _{j = 1}^{n} ( B _{j} - B ) ^{2}}{m + n - 2} = \frac{( m - 1 ) s _{A}^{2} + ( n - 1 ) s _{B}^{2}}{m + n - 2} .

For ten observations in each group,

S^{2} = (s_{A}^{2} + s_{B}^{2}) /2

18

statistical degrees of freedom, provided the assumed independence between groups is justified.

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