Question 1204123: 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 95% confidence assuming s=12.3 based on earlier studies? Suppose the doctor would be content with 95% confidence. How does the decrease in confidence affect the sample size required?
A 99% confidence level requires
enter your response here subjects. (Round up to the nearest subject.)
Answer by math_tutor2020(3816)   (Show Source):
You can put this solution on YOUR website!
E = 3 = desired error
sigma = 12.3 = population standard deviation
At 95% confidence, the z critical value is approximately z = 1.960
This is something to memorize.
Alternatively you can use a Z table or stats calculator (such as a TI83).
n = sample size
n = (z*sigma/E)^2
n = (1.96*12.3/3)^2
n = 64.577296
n = 65
Always round UP to the nearest whole number when it comes to min sample size problems like this.
The minimum sample needed is 65 people, when dealing with 95% confidence.
At 99% confidence, the z value is now z = 2.576
The other values are kept the same.
n = (z*sigma/E)^2
n = (2.576*12.3/3)^2
n = 111.54739456
n = 112
The min sample needed is now 112 people, when dealing with 99% confidence.
A decrease in confidence (from 99% to 95%) reduces the minimum required sample size from 112 people to 65 people.
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