Question 12 A study titled "Heat Stress Evaluation and Worker Fatigue in a Steel Plant" (American Industrial Hygiene Association, Vol. 64, pp. 352-59) assessed fatigue in steel-plant workers due to the heat stress. A random sample of 29 casting workers had a mean post-work heart rate of 78.3 beats per minute (bpm). Assume that the population standard deviation of post-work heart rates for casting workers is 11.2 (bpm). You want to test that the mean post-work heart rate for casting workers exceeds the normal resting heart rate of 72 bpm?

(a) Write down appropriate null and alternative hypotheses to test that the mean post-work heart rate for casting workers exceeds the normal resting heart rate of 72 bpm.

(b) Do the data provide enough evidence to conclude that at5% significance level the mean post-work heart rate for casting workers exceeds the normal resting heart rate of 72 bpm?

(c) Calculate p value and explain.