The owner of a dry cleaning store believes that the mean amount a customer spends on a dry cleaning order exceeds $21.83. 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 $23.91, or X > 23.91. It is assumed that the standard deviation in the bill amounts is $12.95 ( = 12.95). (a) Choose the correct statistical hypotheses. A. H : A = 21.83 Ha: >21.83 B. Ho : a > 21.83, C. Ho X 23.91, D. Ho: X=21.83, E. H: X = 21.83, F. H : |= 21.83, G. HoX> 23.91, : Ha: 23.91 HA: X> 21.83 HA : X 21.83 HA:@#21.83 HA X 23.91 : (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 $21.86. 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 n = 200 and regulate P(Type I) = 0.05. For what values of X should the null hypothesis in (a) be rejected? A. Reject the null hypothesis if X > 43.13 B. Reject the null hypothesis if X > 23.34 C. Reject the null hypothesis if > 43.13 D. Reject the null hypothesis if > 23.34 E. Reject the null hypothesis if > 23.96 F. Reject the null hypothesis if X > 23.91 G. Reject the null hypothesis if X> 21.83 H. Reject the null hypothesis if X > 23.96