The advertisement says that there is 200mL of milk in one bottle. Amy, suspicious of the advertisement, bought 5 bottles and found out each bottle contains 198.2mL, 201.3mL, 196.8mL, 194.9mL, and 194mL, respectively. Given that the distribution is normal with the standard deviation of 2mL, answer the following questions.

1. If the sample mean is same as that of the population, calculate the 95% confidence interval.

2. State the hypothesis on whether Amy is right to say the bottle contains less than 200mL of milk. Then, test the hypothesis with an alpha level of 0.05.

3. Given that the alpha level is 0.05 and the sample mean is 198, what sample size of bottles are needed in order to get a power of 95%?

4. Given that the alpha level is 0.05 and the sample mean is 198, find out the probability of committing a type I error and a type II error.