Q2) Independent-Samples t-Test (15 points total)

**Round calculated results to the hundredth (2^nd place to the right of the decimal)**

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 = .05.

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

Q2a. What is the dependent (outcome) variable? What is the independent (grouping) variable?

Q2b. Create the null and alternative hypotheses (non-directional) for this study, using both words and symbol notation

	Written	Symbolic Symbol bank for copy & pasting: =<>m
Null		H0:
Alternative		H1:

Q2c. Calculate M₁andM₂

Q2d. Calculate df₁, df₂, and df_total

Q2e. Calculateestimated variance for population 1 (₁²) and estimated variance for population 2 (₂²)

Q2f. Calculate the pooled variance (S_pooled²) from the two population variances (from question e above)

Q2g. 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)

Hint: Sampling distribution is derived from the original population, and it consists of means of all possible samples drawn from the original population.

Q2h. Calculate standard deviation (S_diffmean)of the comparison distribution

Hint: This comparison distribution consists of differences between all possible sample means drawn from the two sampling distributions. Its standard deviation is the denominator of the t statistic formula.

Q2i. Calculate the t statistic

Q2j. 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.

Q2k. Compare the calculated tstatistic with the critical tvalue 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.

Q2l. 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.

Q2m. Based on the hypothesis test, is there a significant difference in education level between the males and the females in the sample?