3. an article in time describing various aspects of american life indicated that higher educational achievement paid off. college grads worked 7.4 hours per day, fewer than those with less than a college education.

suppose that the average work day for a random sample of n=100 individuals who had less than a 4- year college education was calculated to be 7.9 hours with a standard deviation of s=2.9 hours.

conduct a hypothesis test that the average number of hours worked by individuals having less than a college degree is greater than individuals having a college degree.

a. what are your null and alternative hypotheses?

b. write down your test statistic and rejection region that should be used with a 95% confidence level. conclude whether or not you can reject the null hypothesis.

c. compute the p-value that the average number of hours worked by individuals having less than a college degree is greater than individuals having a college degree. conclude whether or not you can reject the null hypothesis.

d. in part c, if we had used a significance value of α = .01 would our conclusion be the same? what about at the α = .1 significance level?

e. calculate the probability of a type two error p(accept h0) when µ = 8.1 (at the 95% confidence level).