Question

1. The manufacturer of a portable music player (PMP) has shown that the average life of the product is 72 months with a standard deviation of 12 months. The manufacturer is considering using a new parts supplier for th PMP's and want to test that the new hard drives will increase the life of the PMP. Before manufacturing the PMP's on a lareg scale, the manufactuer sampled 200 PMP's and found the 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 the standard deviation of the older model.
2. A website developer has indicated to potential clients that for the sites he has developed visitors spend an average of 45 minutes per day on the sites. One of his potential clients conducted a survey of 20 visitors to several of his sites and found that the average time spent was 35 minutes with a standard deviation of 7 minutes. Determine if there is sufficient evidence to conclude that the average time spent on the sites is different from what he indicated. Conduct the test at the 0.05 level.
3. In both cases, in addition to testing the hypotheses using a critical value, also calculate the p value for the test statistic.

Answer 1

a)

H0: =72; the new hard drives will not increase the life of PMPs ( i.e., life will remain the same )

H1: > 72; the new hard drives will increase the life of PMPs (right tail)

n=200 ( sample size)

since the sample size is quite large, the test statistics is given by:

b)

H0: =45; visitors spend an average of 45 minutes per day on the sites

H1:45; visitors do not spend an average of 45 minutes per day on the sites ( different from 45 minutes) (two-tail test)

since the sample size is small (<30), the test statistics is given by:

P-value: