Question

**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? **