Question

can some one help with part B) it is not correct, when all my other questions are...

Entered Answer Preview Result B B correct 0.212 0.212 correct 0.661 0.661 incorrect B B correct At least one of the answers above is NOT correct. (1 point) The owner of a dry cleaning store believes that the mean amount a customer spends on a dry cleaning order exceeds $22.27. 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 $23.25, or X > 23.25. It is assumed that the standard deviation in the bill amounts is $12.26 (o = 12.26). (a) Choose the correct statistical hypotheses. A. HO : X = 22.27, HA: X > 22.27 B. HO: H = 22.27 HAN > 22.27 C. Ho: X > 23.25, HA: X S 23.25 D. HO : X = 22.27, HA: X 22.27 E. Hou > 22.27, HAN <22.27 F. Hou = 22.27. HAN 22.27 G. Ho : X = 23.25, HA:X > 23.25 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 1) = 0.212 (c) Unknown to anyone, suppose the mean amount spent by all his customers is $22.78. Find the probability that the owner will conclude that the mean amount a customer spends on a dry cleaning order exceeds $22.27 (his original belief) is correct. Use at least three decimals in your answer. Answer = 0.661 (d) Suppose the statistician decides to change the sample size to n = 200 and regulate P(Type 1) = 0.05. For what values of X should the null hypothesis in (a) be rejected? A. Reject the null hypothesis if u > 42.44 B. Reject the null hypothesis if X > 23.7 C. Reject the null hypothesis if u > 24.29 D. Reject the null hypothesis it X > 22.27 E. Reject the null hypothesis if X > 23.25 F. Reject the null hypothesis if u > 23.7 G. Reject the null hypothesis if X > 42.44 H. Reject the null hypothesis if X > 24.29 Preview My Answers Submit Answers

Answer 1

a)

Null and Alternative Hypothesis:

H₀: µ = 22.27

H₁ : µ > 22.27

b)

Test statistic:

z = (x̅- µ)/(σ/√n) = (23.25 - 22.27)/(12.26/√100) = 0.7993

p-value = 1- NORM.S.DIST(0.7993, 1) = 0.2120

Type I error = 0.212

c)

If true µ₁ = 22.78, then Power, 1 - β =

1 - β = P(X̅ ≥ 23.25 | µ₁ = 22.78)

= P(Z ≥ (23.25 - 22.78)/(12.26/√100) )

= P(Z ≥ 0.38)

= 1 - P(Z < 0.38)

Using excel function :

= 1 - NORM.S.DIST(0.38, 1)

= 1 - 0.6493 = 0.3507