2. Suppose that you got the following summary statistics for biomarker measureme

Question

2. Suppose that you got the following summary statistics for biomarker measurements among 15 boys and 15 girls.

Group | Obs Mean Std. Dev.
---------+----------------------------------
females | 15 2.358 2.226
males | 15 1.507 1.766

(a) Calculate the 2-sample t-test with equal variance by hand. Derive the p-value and report the degree of freedom.

(b) If you want to design a future study with 80% power to detect the mean difference between boys and girls, what is the sample size you need for each gender group?

Explanation / Answer

Sample N Mean StDev SE Mean
1 15 2.36 2.23 0.57
2 15 1.51 1.77 0.46

Difference = mu (1) - mu (2)
Estimate for difference: 0.851000
95% CI for difference: (-0.651832, 2.353832)
T-Test of difference = 0 (vs not =): T-Value = 1.16 P-Value = 0.256 DF = 28
Both use Pooled StDev = 2.0092

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