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1. Suppose the distribution of cholesterol level in normal adults is roughly symmetric with mean 219 mg/100mL and standard deviation 41 mg/100mL. A large number of physicians join a study. Each of them selects a random sample of size 25 from their regular visitors and measures their cholesterol level.
a. What is the expected value of the sample means?
b. What is the standard error of the sample means?
c. What proportion of the sample means do you expect to be greater than 223 mg/100mL?
d. If each physician increases the sample size from 25 to 50, what proportion of the sample means do you expect to be less than 218 mg/100mL?
e. One physician observes the following data on 25 individuals. She does not know the population mean or population variance of cholesterol levels. What is her estimate of the population mean and a 95% confidence interval?
213 196 267 194 249 275 277 165 164 239
190 234 161 214 215 239 225 232 160 261
170 308 160 201 203
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