A salon wants to conduct a survey in order to study the consumption pattern of its consumers. The population mean spending on visiting salon per month is unknown with the population standard deviation is assumed to be $200. A random sample of 55 customers is selected and the sample mean spending on visiting salon per month is $800.
(a) Construct a 95% confidence interval estimate for the population mean spending by a customer on visiting salon per month.
(b) It is suggested to do the second round inspection. This time, the sample size is 120. What is the sampling error at 95% confidence level?