Data Set 21 in Appendix B includes a simple random sample of 37 weights ofpost-1983 pennies. Those 37 weights have a mean of 2.49910 g and a standard deviation of 0.01648g. U.S. Mint specifications require that pennies be manufactured so that the mean weight is 2.500g. A hypothesis test will verify that the sample appears to come from a population with a mean of 2.500 g as required, but use a 0.05 significance level to test the claim that the population of weights has a standard deviation less than the specification of 0.0230 g.
Identify the null hypothesis, alternative hypothesis, test statistic, P-value or critical value(s), conclusion about the null hypothesis, and final conclusion that addresses the original claim. Assume that a simple random sample is selected from a normally distributed population.