Economists studying income distribution in a large town, survey a simple random sample of n=63 households and collect the following sample statistics:

• Mean household income,I- =$37,400
• Standard deviation,sI=$9,700.

(1) Use this data to find a 95%-confidence interval for the mean household income (I) of the entire town.

(2) Use the same data to test the claim that the mean household income in the town is less than $40,000, including the following steps.

• (a) State the hypotheses for the test in terms of the appropriate parameter.
• Use a 5% significance level.
• (b) Find the value of the test-statistic.
• (c) Find the p-value for the test.
• (d) State your decision, and justify it.
• (e) What is your conclusion?