3. The distribution of number of hours students sleep daily in their senior year is assumed to be normal and its mean is believed to be 5 hours. A survey of 15 seniors in the College of Science shows that their sleeping times has an average of 5.8 hours with a standard deviation of 1.28 hours. Test whether the sleeping hours of senior students is more than the general belief? please show the work

(a) State the null hypothesis and alternative hypothesis

(b) Find the test statistic (c) (2 points) If the type-I error = 0.05, find the critical value(s) and shade the rejection region(s)

(d) Base on the type-I error and rejection region(s), given above, what is you