(1 point) The owner of a dry cleaning store believes that the mean amount a cust
ID: 3040250 • Letter: #
Question
(1 point) The owner of a dry cleaning store believes that the mean amount a customer spends on a dry cleaning order exceeds $22.28. 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 $23.35, or X > 23.35. lt is assumed that the standard deviation in the bill amounts is $12.35 ( = 12.35) (a) Choose the correct statistical hypotheses. A. Ho : > 22.28, HA : 22.28 c. Ho : X- 22.28, HA:X>22.28 D. Ho : = 22.28, HA : + 22.28 E. Ho :X = 23.35, HA :X > 23.35 F Ho :X > 23.35, HA : X s 23.35 a. Ho : X = 22.28, HA : X + 22.28 (b) What is the probability of making a Type l 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 $22.95. Find the probability that the owner will conclude that the mean amount a customer spends on a dry cleaning order exceeds $22.28 (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 23.72 B. Reject the null hypothesis if > 42.59 C. Reject the null hypothesis if X > 23.35 D. Reject the null hypothesis if X > 42.59 E. Reject the null hypothesis if > 24.31 E Reject the null hypothesis if > 23.72 G. Reject the null hypothesis if X > 24.31 H. Reject the null hypothesis if X > 22.28Explanation / Answer
a)
option B is correct
b)
P(type I error)
c) for mean =22.95:
d)
for 0.05 level ; critical z =1.645
hence critical value for rejection =mean +z*Std deviaiton =22.28+1.645*1.235= 24.31
option F is correct
probability = P(X>23.35) = P(Z>0.87)= 1-P(Z<0.87)= 1-0.8069= 0.1931Related Questions
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