An manufacturer states that their energy efficient dishwasher use 3.5 gallons water for each cycle. We randomly selected 8 dishwashers and run one cycle for each. The recorded water usage are: 3.8, 3.7, 3.5, 3.8, 3.6, 3.7, 3.5, 3.3. Assume the distribution of water usage is normal.

1.Calculate 98% two-sided confidence interval for the mean water usage.

2.If we request the bound on the error of estimation of the 95% confidence interval to be 0.1, find the minimum sample size. Population standard deviation is assumed to be 0.3.

3.Use the reject region method to test if the average water usage of the dishwasher is larger than 3.5 gallons. Let significance level to be 0.01.