The owner of a dry cleaning store believes that the mean amount a customer spends on a dry cleaning order exceeds $2103. A statistician has said to him that he can be statistically sure that his bellef is true if the mean amount of 100 randomly chosen customer bills is greater than $23.94, or X > 23,94. It is assumed that the standard deviation in the bill amounts is $12.91 (o = 12.91). (a) Choose the correct statistical hypotheses. O A. Ho : /= 21.83 HAIN > 21.83 O B. Ho : X 3 23.94, HA : X $ 23.94 O C. Ha : H = 21.83, HA : M / 21.83 O D. Hot A > 21.83, HAIN 23.94 OF. H. : X - 21.83, HA : X > 21.83 OOH. : X = 21.83, HA: X / 21.83 (b) What is the probability of making a Type I error, using the statistician's criterion? Use at least three decimals in your answer. P(Type D)= [c) Unknown to anyone, suppose the mean amount spent by all his customers is $22.28. Find the probability that the owner will conclude that the mean amount a customer spends on a dry cleaning order exceeds $21.83 (his original belief) is correct. Use at least three decimals in your answer. Answer = (d) Suppose the statistician decides to change the sample size to i - 200 and regulate P(Type !) - 0.05. For what values of X should the null hypothesis In (al be rejected? O A. Reject the null hypothesis if X > 23.95 B. Reject the null hypothesis if X > 23.83 O C. Reject the null hypothesis if j > 23.33 Q D. Reject the null hypothesis in X > 23.94 O-E. Reject the null hypothesis if /4 5 23,95 F. Reject the null hypothesis if X > 21.83 G. Reject the null hypothesis if X > 43.07 OH. Reject the null hypothesis if / 5 43,07