(1 point) The owner of a dry cleaning store believes that the mean amount a cust

Question

(1 point) The owner of a dry cleaning store believes that the mean amount a customer spends on a dry cleaning order exceeds $22.24. 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 tharn $23.03, or X > 23.03. It is assumed that the standard deviation in the bill amounts is $12.37 ( = 12.37) (a) Choose the correct statistical hypotheses. A. H0 : X = 22.24, HA . X 22.24 B. Ho : X = 22.24, HA : X > 22.24 c, Ho : > 22.24, HA : 2224 E. Ho : = 22.24, HA : 22.24 F. Ho X > 23.03, Ha : X 23.03 OA. (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)a- (c) Unknown to anyone, suppose the mean amount spent by all his customers is $22.05. Find the probability that the owner will conclude that the mean amount a customer spends on a dry cleaning order exceeds $22.24 (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 (Type 1) = 0.05. For what values of X should the null hypothesis in (a) be rejected? A. Reject the null hypothesis if X > 23.68 B. Reject the null hypothesis if X > 22.24 C. Reject the null hypothesis if > 2427 D. Reject the null hypothesis if > 42.59 E. Reject the null hypothesis if X > 42.59 F. Reject the null hypothesis if X > 24.27 G. Reject the null hypothesis if X > 23.03 H. Reject the null hypothesis if > 23.68

Explanation / Answer

a)

option D is correct

b)

P(type I error)

c)

for mean =22.05:

probability of rejecting:

d)

here for n=200;

for 0.05 level and right tailed test; critical z =1.6449

hence rejecting region Xbar>22.24+1.6449*0.8747 ~ 23.68

option A is correct.

here mean=       = 22.240 std deviation   == 12.37 sample size       =n= 100 std error=x=/n= 1.2370

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