The average height of women is y = 64 inches, the average height of men is y = 6

Question

The average height of women is y = 64 inches, the average height of men is y = 67 inches. For both the standard deviation is about s = 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?

(b) Now repeat using a sample of 117 men and 117 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 a pretty good idea if there's a difference).

Explanation / Answer

a) std error =std deviation/(7)1/2 =3/(7)1/2 =1.339

for 95% CI; z=1.96

hence for female 95% CI of mean height =mean -/+ z*std error =61.78 to 66.22

for male 95% CI of mean height =mean -/+ z*std error =64.78 to 69.22

from abvoe wei can see that confidence intervals overlap

b)

std error =std deviation/(117)1/2 =3/(117)1/2 =0.2774

for 95% CI; z=1.96

hence for female 95% CI of mean height =mean -/+ z*std error =63.46 ; 64.54

for male 95% CI of mean height =mean -/+ z*std error =66.46 ; 67.54

from above confidence interval does not overlap

as we are increasing the sample size ; the variability around mean will decrease which will give precise interval of values to contain mean values. as interval got shortened overlapping ceased to happen,

we can see that as sample size increases the differnece between two gruoups become more significant,

from abvoe wei can see that confidence intervals overlap

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