In an analysis investigating the usefulness of pennies, the cents portions of 82 randomly selected credit card charges from students are recorded, and they have a mean of 47.6 cents and a standard deviation of 32.8 cents. If the 99 cents are all equally likely, the mean is expected to be 49.5 cents and the population standard deviation is expected to be 28.866 cents. Use a 0.01 significance level to test the claim that the sample is from a population with a to 28.866 cents.
Identify the null and alternative hypotheses
Compute the test statistic
Find the P-value of the test statistic
State the conclusion