It is believed that the average US households spending on food is 39 dollars per day. Suppose you recently take a random sample of 81 households in the US and the result revealed a mean of 41 dollars per day with the standard deviation of 2 dollars.

a. (15 points out of 100) Can it be concluded that the average dollars spent per day by U.S. households has changed? (please provide 2 approached both the T-test (Zscore) and P-value approach. (You should write down the null, alternative, formulas, and provide your p-value on the z graph.) (Each approach has 7.5 points)

b. (10 points out of 100) Create the 95 % Confidence Interval for the population mean using the information above? (Do not forget the complete formula of the interval)