Question

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 3 points with 99% confidence assuming s = 11.1 based on earlier studies? Suppose the doctor would be content with 95% confidence. How does the decrease in confidence affect the sample size required? 5 Click the icon to view a partial table of critical values. A 99% confidence level requires subjects. (Round up to the nearest subject.) Partial Critical Value Table Critical Value, Za/2 Level of Confidence, (1 - a) • 100% 90% 95% 99% a Area in Each Tail, – 0.05 0.025 0.005 1.645 1.96 2.575 Print Done

Answer 1

Here we have ME =3, 0 =11.1,CL =0.99 Level of significance: a=0.01 Critical value of z is 21-a/2 =2.576 Required sample size is: 10/2.02 2 ME - =((2.576*11.1)/3)^2 = 90.84377344 Hence, the required sample size is 91. Excel function for critical value: ENORMSINV(1-(0.01/2))

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For 95% confidence level:

Here we have ME =3, 0 =11.1,CL =0.95 Level of significance: a=0.05 Critical value of z is 21-a/2 =1.96 Required sample size is: n= 1-4/2.0 - =((1.96*11.1)/3)^2 = 52.591504 Hence, the required sample size is 53. Excel function for critical value: ENORMSINV(1-(0.05/2))

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As the confidence level decreases, sample size also decrease.