John wants to compare two means. His sample statistics were $\bar { x } _ { 1 } = 22.7 , s _ { 1 } ^ { 2 } = 5.4 , n _ { 1 } = 9$ and $\bar { x } _ { 2 } = 20.5 , s _ { 2 } ^ { 2 } = 3.6 , n _ { 2 } = 9$ . Assuming equal variances, the test statistic is:
A)2.37
B)2.20
C)1.96
D)Must know ? to answer.

Question

Quizplus · Accepted Answer

The test statistic for a two-sample t-test with equal variances is given by:
$$t=\frac{\bar{x}_1-\bar{x}_2}{\sqrt{\frac{s_1^2+s_2^2}{n_1+n_2-2}}\sqrt{\frac{1}{n_1}+\frac{1}{n_2}}}$$
Plugging in the given numbers, we get:
$$t=\frac{22.7-20.5}{\sqrt{\frac{5.4+3.6}{9+9-2}}\sqrt{\frac{1}{9}+\frac{1}{9}}}$$
Simplifying, we get:
$$t=2.20$$
Therefore, the answer is B.

John Wants to Compare Two Means xˉ1=22.7,s12=5.4,n1=9\bar { x } _ { 1 } = 22.7 , s _ { 1 } ^ { 2 } = 5.4 , n _ { 1 } = 9xˉ1​=22.7,s12​=5.4,n1​=9

John Wants to Compare Two Means $\bar { x } _ { 1 } = 22.7 , s _ { 1 } ^ { 2 } = 5.4 , n _ { 1 } = 9$