1. Why can you never really have 100% confidence of correctly estimating the population characteristic of interest?

2. When should you use the t distribution to develop the confidence interval estimate for the mean?

3. Why is it true that for a given sample size, n, an increase in confidence is achieved by widening (and making less precise) the confidence interval?

4. The manager of a paint supply store wants to estimate the amount of paint contained in 1-gallon cans purchased from a nationally known manufacturer. The manufacturer'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 can 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)?

5. The column 'Sedans' contains the overall miles per gallon (MPG) of 2012 family sedans.

a) Construct a 95% confidence interval estimate for the population mean MPG of 2012 family sedans, assuming a normal distribution.

b) Interpret the interval constructed in (a).

6. The column 'SUV' contains the overall miles per gallon (MPG) of 2012 small SUVs.

a) Construct a 95% confidence interval estimate for the population mean MPG of 2012 small SUVs, assuming a normal distribution.

b) Interpret the interval constructed in (a).

c) Compare the results in (a) to those in Problem 8.19(a).

7. If the manager of a paint supply store wants to estimate, with 95% confidence, the mean amount of paint in a 1-gallon can to within ±0.004 gallon and also assumes that the standard deviation is 0.02 gallon, what sample size is needed?

Attachment:- Data.xlsx