Test the following claim. Determine the null hypothesis, alternative hypothesis, test statistic, critical value, conclusion regarding the null hypothesis, and final conclusion that adress original claim.
A manual states that in order to be a hit, a song should be no longer that three minutes and thirty seconds (or 210 seconds). A simple random sample of 50 current hit songs resluts in mean length of 252.5 sec. Suppose the population standard deviation of song length is 54.5 sec. Employ a 0.01 significance level to test the claim that the sample is from population of songs with the mean greater than 210 sec. What do these results consider about the advice given in the manual?