You would like to construct a 95% confidence interval to estimate the population mean score on a nationwide examination in finance, and for this purpose, we choose a random sample of exam scores. The sample we choose has a mean of 511 and a standard deviation of 76.
(a) What is the best point estimate, based on the sample, to use for the population mean?
(b) For each of the following sampling scenarios, determine which distribution should be used to calculate the critical value for the 95% confidence interval for the population mean.
- The sample has size 14, and it is from a normally distributed population with an unknown standard deviation.
- The sample has size 90, and it is from a non-normally distributed population with a known standard deviation of 76.
- The sample has size 10, and it is from a population with a distribution about which we know very little.