In a large-scale, cost-of-living survey undertaken last January, weekly grocery expenses for families with one or two children were found to have a mean of $148 and a standard deviation of $25. To investigate the current situation, a random sample of families with one or two children is to be chosen and their last week's grocery expenses are to be recorded.
(a) How large a sample should be taken if one wants to be 95% sure that the error of estimation of the population mean grocery expenses per week for families with one or two children does not exceed $2? (Use the previous s as an estimate of the current cr.)
(b) A random sample of 100 families is actually chosen, and from the data of their last week's grocery bills, the mean and the standard deviation are found to be $155 and $22, respectively. Construct a 98% confidence interval for the current mean grocery expense per week for the population of families with one or two children.