Question

Assume you are conducting a 2 independent samples t-test with the following information

	SAMPLE 1	SAMPLE 2
SAMPLE SIZE (n)	30	25
SAMPLE MEAN	42	39

The pooled estimate of the common variance is 18.

What is the value of the test statistic, t_c ? Include 2 decimal places in your answer.

Answer 1

The hypothesis for the problem is

Null Hypothesis:

Alternate Hypothesis:

The t statistic for 2 independent samples using the pooled common variance is given by the below formula.

We have pooled variance ,

and

and

Thus using the above formula,

t = (42-39) / = 2.61

Let us assume a significance level

and df = n1+ n2 - 2 = 30 + 25 -2 = 53

Using the t table we find tc 2.00

Since the t-calculated is greater than tc, we reject the null hypothesis.