Step 1 :A doctor wants to estimate the mean HDL cholesterol of all 20 - to 29 -year-old females. The doctor wants to estimate this within 2 points with a confidence level of 99% and 90%. The standard deviation, based on earlier studies, is 15.7.
Step 2 :For a 99% confidence level, the required sample size is 409 subjects. This is rounded up to the nearest subject.
Step 3 :For a 90% confidence level, the required sample size is 167 subjects. This is also rounded up to the nearest subject.
Step 4 :The question asks how the sample size required changes when the confidence level decreases. The confidence level is the probability that the confidence interval contains the true population parameter.
Step 5 :A higher confidence level means that there is a higher probability that the confidence interval contains the true population parameter, but it also means that the confidence interval is wider. Therefore, to maintain the same level of precision, a larger sample size is needed.
Step 6 :Conversely, a lower confidence level means that the confidence interval is narrower, so a smaller sample size is needed to maintain the same level of precision.
Step 7 :\(\boxed{\text{Final Answer: B. Decreasing the confidence level decreases the sample size needed.}}\)