The owner of a dry cleaning store believes that the mean amount a customer spends on a dry cleaning order exceeds $21.84. A statistician has said to him that he can be statistically sure that his belief is true if the mean amount of 100 randomly chosen customer bills is greater than $23.46, or X > 23.46. It is assumed that the standard deviation in the bill amounts is $12.06 (o = 12.06). (a) Choose the correct statistical hypotheses. OA. Ho : X = 21.84, HA : X / 21.84 B. Ho : /4 = 21.84 HA : / > 21.84 C. Ho: / = 21.84, HA : p / 21.84 D. Ho : p > 21.84, HA : u 23.46 F. Ho : X > 23.46, HA : X 21.84 (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 I) = (c) Unknown to anyone, suppose the mean amount spent by all his customers is $21.79. Find the probability that the owner will conclude that the mean amount a customer spends on a dry cleaning order exceeds $21.84 (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 n = 200 and regulate P(Type /) = 0.05. For what values of X should the null hypothesis in (a) be rejected? A. Reject the null hypothesis if X > 23.24 B. Reject the null hypothesis if X > 41.68 C. Reject the null hypothesis if u > 23.24 D. Reject the null hypothesis if X > 21.84 E. Reject the null hypothesis if # > 41.68 F. Reject the null hypothesis if X > 23.46 G. Reject the null hypothesis if X > 23.82 H. Reject the null hypothesis if / > 23.82