gear motor manufacturer wants to test the hypothesis that the mean rotation rate for particular motor under a wide variety of loading is 50 rpm. Assume that the rotation rate is normally distributed. A quality control engineer sets up an experiment where the rotation rate of the motor measured as it is used t0 drive 9 different loads of increasing torque. The sample mean and standard deviation are computed to be X = 45.4 and S = 5. Clearly state the null and alternate hypotheses. ii_ Test the above hypothesis using significance level of0.01. Also, show the test critical region on the distribution (hint: check the lecture slides)_