Question

Suppose the (sample) average height of women is ̄y = 65.5 inches, the average height of men is ̄y = 68.5 inches. For both the sample standard deviation is about s = 3 inches. (a) Suppose you take a sample of 6 women and 5 men. Construct a 95% CI for both. Do the confidence intervals overlap? (b) Now repeat using a sample of 200 men and 215 women. Do the confidence intervals overlap? (c) Can you explain what happened? Why is sample size important if you're trying to find differences between groups? (Statistical comment: comparing CI's is not the correct way of comparing two groups, but it can give you an idea if there's a difference). 6) Use the data for heights that you collected in recitation last week and construct a 99% CI. Use R to do this. While your lecture may not have learned about the t-test yet, a CI is just the reverse of a one sample t-test. To get 95% Confidence intervals in R see the following page

Answer 1

a.

95% confidence interval for women:

95% confidence interval for men:

b.

95% confidence interval for women:

95% confidence interval for men:

c.

From a and b we see that whensample size is small both confidence interval overlap. But when sample size increases confidence interval separeted from each other. This is happens because as we increase sample size standard error get decreased. Hence confidence interval become small.

Hence we conclude that comparing CI's is not the correct way of comparing two groups, but it can give you an idea if there's a difference.