Please show your work and have a good explanation.

The Environmental Protection Agency has determined that safe drinking water should have an average pH of 7 moles per liter. You are testing water from a new source, and take 30 vials of water. Water is unsafe if it deviates too far from 7 moles per liter in either direction. The mean pH level in your sample is 6.4 moles per liter, which is slightly acidic. The standard deviation of the sample is 0.5 moles per liter. (a) Do the data provide convincing evidence at the a = 0.05 level that the true mean pH of water from this source differs from 7 moles per liter? (Do in State, Plan, Do, and Conclude Format) (b) A 95% confidence interval for the true mean pH level of the water is (6.21, 6.59) . Interpret this interval. (c) Explain why the interval in part (b) is consistent with the result of the test in part (a). (d) The power of the test to detect / = 6.8 is 0.59. Interpret this value. (Make sure you use the precise wording (e) Give one way to increase the power of this test