A simple random sample of 37 weights of post-1983 pennies have a mean weight of 2.49910g and a standard deviation of .01648g. U.S. Mint specifications require that pennies be manufactured so that the mean weight is 2.500g. A hypothesis will verify that the sample appears to come from a population with a mean of 2.500 as required, but use a .05 significance level to test the claim that the population of weights has a standard deviation less than the specification of .0230g.
Identify null hypothesis, alternative hypothesis, test statistic, p-value or critical value(s), conclusion about null hypothesis, and final conclusion that addresses the original claim. Assume that a simple random sample is selected from a normally distributed population.