Discussion:
Q1. If X=85 (sample mean), 8 is population standard deviation, and n=64 is sample size, construct a confidence interval estimate for the population mean.
Q2. The manager of a paint supply store wants to estimate the actual amount of paint contained in 1-gallon cans purchased from a nationally known manufacturer. The manufactuer's specifications state that the standard deviation of the amount of paint is equal to 0.02 gallon. A random sample of 50 cans is selected, and the sample mean amount of paint per 1-gallon is 0.995 gallon.
a. Construct a 99% confidence interval estimate for the population mean amount of paint included in a 1-gallon can.
b. On the basis of these results, do you think that the manager has a right to complain to the manufacturer? Why?
c. Must you assume that the population amount of paint per can is normally distributed here? Explain.
d. Construct a 95% confidence interval estimate. How does this change your answer to (b)?
Q3. A stationary store wants to estimate the mean retail value of greeting cards that it has in its inventory. A random sample of 100 greeting cards indicates a mean value of $2.55 and a standard deviation of $0.44.
a. Assuming a normal distribution, construct a 95% confidence interval estimate for the mean value of all greeting cards in the store's inventory.
b. Suppose there were 2, 500 greeting cards in the store's inventory. How are the results in (a) useful in assisting the store owner to estimate the total value of the inventory?
Q4. CareerBuilder.com surveyed 1,124 mothers who were currently employed full time. Of the women surveyed, 281 said that they were dissatisfied with their work-life balance, and 495 said that they would take a pay cut to spend more time with their kids.
a. Construct a 95% confidence interval estimate for the population of mothers employed full time who are dissatisfied with their work-life balance.
b. Construct a 95% confidence interval estimate for the population proportion of mothers employed full time who would take a pay cut to spend more time with their kids.