Researchers collected a simple random sample of the times that 81college students required to earn their bachelor’s degrees. The sample has a mean of 4.8 years and a standard deviation of 2.2 years (based on data from the National Center for Education Statistics). Use a 0.05 significance level to test the claim that the mean time for all college students is greater than 4.5 years.

Assume that a simple random sample has been selected from a normally distributed population and test the given claim. Unless specified by your instructor, use either the traditional method or P-value method for testing hypotheses. Identify the null and alternative hypotheses, test statistic, P-value (or range of P-values), critical value(s), and state the final conclusion that addresses the original claim.