A city assessor wished to estimate the mean income per household. The previous mean income was $25,300. A random sample of 40 households in the city showed a mean income of $29,400 and a standard deviation of $6325.
(a) Find a 95% confidence interval for, the population mean income per household in the city.
(b) Based on your answer in part (a), would the assessor conclude that the mean income had increased over the previous estimate of $25,300?