Question

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 = 15.7 based on earlier studies? Suppose the doctor would be content with 95% confidence. How does the decrease in confidence affect the sample size? 99% requires ??? subjects 95% requires ???? subjects How does the decrease in confidence affect the sample size?

Answer 1

Answer:-

Given That:-

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 = 15.7 based on earlier studies? Suppose the doctor would be content with 95% confidence. How does the decrease in confidence affect the sample size? 99% requires ??? subjects 95% requires ???? subjects How does the decrease in confidence affect the sample size?

Given,

Population standard deviation = = 15.7

Margin of error = E = 2

How does the decrease in confidence affect the sample size? 99% requires ???

At 99% confidence level the z is ,

= 1 - 99%

= 1 - 0.99

= 0.01

/ 2 = 0.01 / 2

= 0.005

Z/2 = Z0.005

= 2.576

sample size = n =

n = (2.576 * 15.7 / 2)2

n = 408.91

n = 409

Sample size = 409

A 99% confidence level requires 409 subjects.

subjects 95% requires ???? subjects

At 95% confidence level the z is ,

= 1 - 95%

= 1 - 0.95

= 0.05

/ 2 = 0.05 / 2

= 0.025

Z/2 = Z0.025

= 1.96

sample size = n =

n = (1.96 * 15.7 / 2)2

n = 236.73

n = 237

Sample size = 237

A 95% confidence level requires 237 subjects.

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