Question 1137977: A doctor wants to estimate the mean HDL cholesterol of all 20- to 29-year-old females. How many subjects are needed to estimate the mean HDL cholesterol within 2 points with 99 % confidence assuming s equals 19.2 based on earlier studies? Suppose the doctor would be content with 90 % confidence. How does the decrease in confidence affect the sample size required?
A 99% confidence level requires....BLANK....subjects?
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! 99%CI is tdf=?, 0.995*s/sqrt(n); 2=t*19.2/sqrt(n)
square both sides and move the sqrt(n) over
4n=t^2*19.2^2
n=t^2(368.64/4)=t^2*92.16
Since the t-value will be at least 2 and probably larger, the sample size will be a minimum of 370. At that size, z can be used
half-interval of 2=1.96*19.2/sqrt(n)
4n=1.96^2*19.2^2
n=354.04 or 355.
The decrease in the confidence interval t 90% changes the t/z value to 1.645, and that is about 5/8 as much as the 99% confidence
Because we are dealing with squares here, that will be about 25/64 or just under 40% of the prior sample size. Lower confidence allows smaller samples, all else remaining constant.
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