A study about the lead concenstration of water in a water district takes water samples from a random sample of 61 independent observations. A recent guideline requires the lead con- centration to be less than 7 ug/L. We consider the following null and alternative hypotheses for the mean lead amount u in (ug/L): H:H7 versus Hi:<7 (a) (1 pt) Assume that the sample mean of these 61 samples is observed to be T = 6.5 pg/L with a sample standard deviation of s = 1.5 ug/L. Find the relevant test statistic (e.g. a z statistic or a t statistic) for this test. Justify your answer for the choice of the test statistic. (b) (1.5 pts) Determine the P-value of the test. Show the work. If you use a technology tool, state which one. (c) (1.5 pts) Based on your answer in parts (c), can you reasonably conclude that the mean lead concentration to be less than 7 mg/L? Use a = 0.02 significance level for this test. Show the work and explain your reasoning.