1)An advertising agency that serves a major radio station wants to estimate the mean amount of time that
the station's audience spends listening to the radio daily. From past studies, the standard deviation is estimated as 40 minutes.
a. What sample size is needed if the agency wants to be 95% confident of being correct to within ±4 minutes?
b. If 99% confidence is desired, how many listeners need to be selected?
2) The management of a soft drink company is interested in determining whether the proper amount of soft drink has been placed in 2-liter bottles at the local bottling plant. The bottling plant has informed the management that the population standard deviation for 2-liter bottles is 0.05 liter. A random sample of one hundred 2-liter bottles selected from this bottling plant indicates a sample mean of 1.978 liters.
a. Use a one-sample hypothesis test to decide whether the mean amount in the bottles is different from 2.0 liters. Use a 0.05 level of significance.
b. Construct a 95% confidence interval estimate of the population mean amount in the bottles.
c. Compare the results of parts (a) and (b). What conclusions do you reach?