Need help with all 3 parts. Thanks 5) The average height of women is y 64 inches
ID: 3333237 • Letter: N
Question
Need help with all 3 parts. Thanks 5) The average height of women is y 64 inches, the average height of men is y- 67 inches. For both the standard deviation is abouts 3 inches. (a) Suppose you take a sample of 7 women and 7 men. Construct a 95% CI for both. Do the confidence intervals overlap? repeat using a sample of 117 men and 117 women. Do the confidence intervals (b) Now overlap? (c) Can you explain what happened? Why is sample size important if you're trying to find differences between groups? Statistical comment: comparing Cl's is not the correct way of comparing two groups, but it can give you a pretty good idea if there's a difference).
Explanation / Answer
a. The 95% c.i for population mean height of men:xbar+-talpha/2, df=n-1 (s/sqrt n), where, xbar is sample mean, t i st critical at n-1 df and alpha/2 (alpha=0.05, alpha/2=0.025), s is sample standard deviation, n is sample size.
=64+-2.447(3/sqrt 7)
=(61.23, 66.27)
Equivalently, the 95% c.i for women is: 67+-2.447(3/sqrt 7)=(64.23, 69.77). The confidence interval does overlap.
b. The 95% c.i for height of men: 64+-2.447(3/sqrt 117)=(63.451, 64.549)
The 95% c.i for height of women: 67+-2.447(3/sqrt 117)=(66.451, 67.549)
The confidence interval does not overlap.
c. For smaller sample sizes, the confidence interval overlaps and for larger sample sizes confidence intervals doesnot overlap. For smaller samples, n<30, one needs to check for normality assumption. If samples are larger, normality asumption holds true and since, degrees of freedom is n1+n2-2, which further determines the critical t, sample size is important in finding difference between two groups.