Assume that a simple random sample has been selected from a normally distribute population and test the given claim. Identify the null and alternative hypotheses, test statistic, P-value, critical value(s), and state the final conclusion that addresses the original claim.

In a manual on how to have a number one song, it is stated that a song must be no longer than 210 seconds. A simple random sample of 40 current hit songs results in a mean length of 242.2 sec and a standard deviation of 53.81 sec. Use a 0.05 significance level and the accompanying Minitab display to test the claim that the sample is from a population of songs with a mean greater than 210 sec. What do these results suggest about the advice given in the manual?

Minitab display

One-Sample T

Test of mu = 210 vs> 210

N 40 Mean 242.20 StDev 53.81 SE Mean 8.51 95% Lower Bound 227.86 T 3.78 P 0.000

What are the hypotheses?