In an effort to determine the mean annual amount spent per customer for groceries at the particular supermarket, data were collected for a sample of 100 households. The sample showed an average amount of $8,000.
If the population standard deviation is $500,
a. develop an 80% confidence interval estimate of the population mean annual amount spent.
b. develop an 85% confidence interval estimate of the population mean annual amount spent.
c. discuss what happens to the width of the confidence interval as the confidence level is increased. Does this seem reasonable? Explain.
d. If the data were collected for a sample of 50 households rather than 100, develop an 85% confidence interval estimate of the population mean annual amount spent, assuming the population has a normal probability distribution.