HELP!! I have no idea to get this answer :(
a doctor wants to estimate the HDL cholesterol of all 20-29 year old females. how many subjects are needed to estimate the HDL cholesterol within 4 points with 99% confidence assuming the standard deviation is 10.8? Suppose the doctor would be content with 95% confidence. How does the decrease in confidence affect the sample size required?
To estimate the required sample size, we can use the formula for sample size calculation in a confidence interval:
n = (Z * σ / E)^2
where:
n = sample size
Z = z-value associated with the desired confidence level (given as 1.96 for 99% confidence and 1.96 for 95% confidence)
σ = standard deviation (given as 10.8)
E = margin of error (given as 4 points)
For 99% confidence:
n = (1.96 * 10.8 / 4)^2
For 95% confidence:
n = (1.96 * 10.8 / 4)^2
To calculate the sample size for each case, let's plug in the values and solve for n:
For 99% confidence:
n = (1.96 * 10.8 / 4)^2 = (21.168 / 4)^2 = 105.84
So, the doctor would need approximately 106 subjects to estimate the HDL cholesterol within 4 points with 99% confidence.
For 95% confidence:
n = (1.96 * 10.8 / 4)^2 = (21.168 / 4)^2 = 105.84
So, even with a decrease in confidence level to 95%, the required sample size remains the same at approximately 106 subjects. Decreasing confidence does not affect the sample size in this case.