Thanks in advance! :) both the standard deviation is about s = 3 inches. (a) Sup

Question

Thanks in advance! :) 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 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

Solution:

a) CI = x1 - x2 ± Z /2 * Sqrt ( sd1^2 / n1 + sd2^2 /n2 )
Mean(x1) = 64
Standard deviation( sd1 ) = 3
Sample Size(n1) = 7
Mean (x2) = 67
Standard deviation( sd2 ) = 3
Sample Size(n2) = 7

CI = [ ( 64-67) ±Z /2 * Sqrt( 9/7+9/7)]
= [ (-3) ± Z /2 * Sqrt( 2.57) ]
= [ (-3) ± 1.96 * Sqrt( 2.57) ]
= [-6.1421 , 0.1421]

b) Sample Size = n1 = n2 =117
CI = [ ( 64-67) ±Z /2 * Sqrt( 9/117+9/117)]
= [ (-3) ± Z /2 * Sqrt( 0.15) ]
= [ (-3) ± 1.96 * Sqrt( 0.15) ]
= [-3.7591 , -2.2408]
yes it is partially overlapped

c) Increasing the sample size narrower the interval, as it indirectly proportional to the confidence.

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