Question

n 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.  

n 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		11	16
2	12		12	16
3	14		13	18
4	12		14	16
5	16		15	16
6	16		16	14
7	12		17	16
8	14		18	12
9	16		19	18
10	16		20	18
			21	16
			22	16

1. Calculate estimated variance for population for population 1 (S1^1) and (S2^2)

2.Calculate the pooled variance (Spooled2) from the two population variances

3.Use the pooled variance (from question f above) to calculate the variance for sampling distribution 1 (SM12) and the variance for sampling distribution 2 (SM22?

4.Calculate standard deviation (Sdiffmean)of the comparison distribution

5. calculate t statistic and critical t values

Answer 1

We are given a two-tailed test.

We will run the t-test for independence in Excel.

Load the data into Excel.

Go to Data>Megastat.

Select the option Hypothesis tests and go to Compare Two Independent Samples.

Select the Group 1 and Group 2 as Education for Male and Education for Female respectively.

Click OK.

The output obtained will be as follows:

Male Education	Female Education
14.00	16.00	mean
1.89	1.71	std. dev.
10	12	n
	20	df
	-2.000	difference (Male Education - Female Education)
	3.200	pooled variance
	1.789	pooled std. dev.
	0.766	standard error of difference
	0	hypothesized difference
	-2.611	t
	.0167	p-value (two-tailed)

1. Calculate estimated variance for population 1 (S1^1) and (S2^2)

s₁ from the output is 1.89

s₂ from the output is 1.71

s₁²= 1.89² = 3.56

s₂²= 1.71² = 2.91

2.Calculate the pooled variance (Spooled2) from the two population variances

Pooled variance from the output is 3.2.

3.Use the pooled variance (from question f above) to calculate the variance for sampling distribution 1 (SM12) and the variance for sampling distribution 2 (SM22?

The variance for sampling distribution 1, SM₁² = S_Pooled²/n₁ = 3.2/10 = 0.32

The variance for sampling distribution 2, SM₂² = S_Pooled²/n₂ = 3.2/12 = 0.27

4.Calculate standard deviation (Sdiffmean)of the comparison distribution

S_diffmean from the output is 1.789.

5. calculate t statistic and critical t values

t statistic, t_stat from the output is -2.611.

The critical values for a significance level, α = 0.1 and df = 20 from a t-table for a two-tailed test are ±1.725.