"E-H" Q2) Independent-Samples t-Test (Round calculated results to the hundredth (2nd 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 α = .10. Male Subject ID Education Female Subject ID Education 1 14 13 14 2 15 14 15 3 17 15 18 4 13 16 18 5 15 17 16
Please answer "E-H"
Q2) Independent-Samples t-Test
(Round calculated results to the hundredth (2nd 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 α = .10.
|
Male Subject ID |
Education |
|
Female Subject ID |
Education |
|
1 |
14 |
|
13 |
14 |
|
2 |
15 |
|
14 |
15 |
|
3 |
17 |
|
15 |
18 |
|
4 |
13 |
|
16 |
18 |
|
5 |
15 |
|
17 |
16 |
|
6 |
15 |
|
18 |
17 |
|
7 |
13 |
|
19 |
16 |
|
8 |
15 |
|
20 |
16 |
|
9 |
15 |
|
21 |
17 |
|
10 |
16 |
|
22 |
15 |
|
11 |
17 |
|
23 |
13 |
|
12 |
14 |
|
24 |
17 |
|
|
|
|
25 |
18 |
|
|
|
|
26 |
17 |
a. What is the dependent (outcome) variable? What is the independent (grouping) variable?
dependent variable: Education
Independent variable: gender
b. Create the null and alternative hypotheses (non-directional) for this study, using both words and symbol notation(1 point total: .5 for each hypothesis, both written and symbol notation need to be correct to earn the credit for each hypothesis)
H0 : u1=u2
That is there is not significant difference between mean education of male and female.
V/S
H1 : u1 not equal to u2
That is there is significant difference between mean education of male and female.
c. CalculateM1and M2 (1 point total: .5 point per sample mean, both process and result must be correct to earn credit for each mean)
i)male mean education= M1= 14.966
ii) female mean education=M2 = 16.2142
d. Calculatedf1, df2, and dftotal (1 point total: deduct .5 for each error)
df1 = 11, df2= 13, df total = 24
e. Calculateestimated variance for population 1 (s1^2) and estimated variance for population 2 (s2^2)
f. Calculate the pooled variance (Spooled2)from the two population variances (from question e above)
g. 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)
Hint: Sampling distribution is derived from the original population, and it consists of means of all possible samples drawn from the original population.
h. Calculate standard deviation (Sdiffmean)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.
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