Question

A sample of 50 females is given a test and they score an average of 75 on it. A sample of 36 males is also given the test and score an average of 72 on it. It is known from previous studies that the females have a standard deviation of 10, while the males have on of 12 on this test. At an alpha of .05 is there a significant difference in the true means for the females and the males?

a. Null/Alternate Hypothesis.

b. Test Statistic.

c. Critical regions

d. Reject/Fail to Reject

e. Find the p-value

f. Answer the question.

Answer 1

a) The test hypothesis is
\\Null\;Hypothesis --> H_0: \mu_1 = \mu_2, or \; H_0: \mu_1 - \mu_2 = 0
\\Alternate\;Hypothesis --> H_1: \mu_1 \ne \mu_2, or \; H_0: \mu_1 - \mu_2 \ne 0
This is a two-sided test because the alternative hypothesis is formulated to detect differences from the hypothesized difference in mean values on either side.
Now, the value of test static can be found out by following formula:

c) Degrees of freedom on the t-test statistic are n1 + n2 - 2 = 50 + 36 - 2 = 84
For .Citical region are (-1.9886, 1.9886)
d) Since , we fail to reject the null hypothesis H0 at .
e) Using Excel's function =T.DIST.2T(|t_0|,n-1), the P-value for t_0 = 1.2617 in an t-test with 84 degrees of freedom can be computed as P =
Since P = 0.2105 > 0.05, we fail to reject the null hypothesis H0 at