You are hired by the u. s. treasury to determine whether a batch of 5 quarters is counterfeit. assume you are told that a standard u. s. quarter has a weight that is normally distributed with mean 5.67 grams and standard deviation 0.02 grams. assume that the weight of counterfeit coins has a distribution with unknown mean and standard deviation. (a) what type of hypothesis test should you use to determine whether the quarters are counterfeit? be specific. write down a null and alternative hypothesis for your test. (b) determine a rejection region for your test at a significance level of alpha = 0.01. (c) assume you measure the weights of the 5 quarters to be 5.68, 5.65, 5.64, 5.63, and 5.61 respectively. what is the value of your test statistic, and what is its p-value? (d) what inference can you make about the null hypothesis at the alpha = 0.01 significance level?