Question

In a research project, researchers collected demographic and health data from a sample of elderly residents in the community. To examine any possible gender differences in their sample, they want to see if the females and the males differ significantly on the education level (number of years of formal schooling). The researchers are not predicting any direction in the possible gender differences so the hypotheses should be non-directional. They would like to run a two-tailed test with α = .10

Male Subject ID	Education		Female Subject ID	Education
1	12		13	16
2	12		14	18
3	14		15	18
4	12		16	16
5	16		17	16
6	16		18	14
7	12		19	16
8	14		20	12
9	16		21	18
10	16		22	18
11	15		23	16
12	13		24	16
			25	18
			26	12

g. Use the pooled variance (from question f above) to calculate the variance for sampling distribution 1 (S_M1²) and the variance for sampling distribution 2 (S_M2²)

d. Calculate df₁ , df₂, and df_total

f. Calculate the pooled variance (S_pooled²) from the two population variances (from question e above)

j. For the two-tailed test, find the critical t values for this hypothesis test based on the total degree of freedom (from question d above), and the preset alpha level. (1 point total)

k. Compare the calculated t statistic with the critical t value by stating which is more “extreme”, and then draw a conclusion about the hypothesis test by stating clearly “reject” or “fail to reject” the null hypothesis. (1 point total: .5 for comparison, .5 for decision)

l. Calculate the pooled standard deviation for the populations (use the pooled variance calculated in question f); and then calculate the standardized effect size of this test. (1 point total: .5 for pooled standard deviation, .5 for effect size. Both process and result must be correct to earn the credit for each item.)

Answer 1

t table as follows: