The Federal Communications Commission released a report (Leslie Cauley, USA Today , “Study: A la Carte Cable Would Be Cheaper,” February 10, 2006) refuting an earlier report released in 2004 by the Federal Communications Commission (FCC) under the prior chairman, Michael Powell. The 2006 report indicates that cable subscribers would save as much as 13% on their cable television bills. The average monthly cable prices were estimated to be $41.04. Typically, such reports announce a margin of error of, say, $1.25 and a confidence level of 95%. Suppose the standard deviation of the monthly cost of cable television bills was $10.00.
a. Determine the sample size of the study released by the FCC in 2006.
b. Calculate the sample size required to decrease the margin of error by a dollar.
c. A typical sample size used in national surveys is 1,500 to 2,000. Determine a range for the margin of error corresponding to this range of sample sizes.