The manufacturer of a portable music player (PMP) has shown thatthe average life of the product is 72 months with a standarddeviation of 12 months. The manufacturer is considering using a newparts supplier for th PMP's and want to test that the new harddrives will increase the life of the PMP. Before manufacturing thePMP's on a lareg scale, the manufactuer sampled 200 PMP's and foundthe average life to be 78 months. Test the hypothesis using alpha =.01 that the new hard drives will increase the life of the PMP's.Assume the standard deviation of the new PMP's is the same as thestandard deviation of the older model.

A website developer has indicated to potential clients that forthe sites he has developed visitors spend an average of 45 minutesper day on the sites. One of his potential clients conducted asurvey of 20 visitors to several of his sites and found that theaverage time spent was 35 minutes with a standard deviation of 7minutes. Determine if there is sufficient evidence to conclude thatthe average time spent on the sites is different from what heindicated. Conduct the test at the 0.05 level.

In both cases, in addition to testing the hypotheses using acritical value, also calculate the p value for the teststatistic.