Help needed asap :) Please and thank you

#1
The owner of a dry cleaning store believes that the mean amount a customer spends on a dry cleaning order exceeds $22.00. 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 $22.49, or X⎯⎯⎯>22.49. It is assumed that the standard deviation in the bill amounts is $2.50 (σ=2.50).

What is the probability of making a Type I error, using the statistician's criterion? Use three decimals in your answer.
P(TypeI) =

c) Unknown to anyone, suppose the mean amount spent by all his customers is $21.75. Find the probability that the owner will conclude that his original belief is correct. Use three decimals in your answer.

I would really appreciate any help!

Thank you very much
 

Dason

Ambassador to the humans
#2
Hi! :welcome: We are glad that you posted here! This looks like a homework question though. Our homework help policy can be found here. We mainly just want to see what you have tried so far and that you have put some effort into the problem. I would also suggest checking out this thread for some guidelines on smart posting behavior that can help you get answers that are better much more quickly.
 
#3
Thank you Dason. Sorry about that. Ive done 2 parts to the question so far.

First being: Choose the correct statistical hypotheses.
A. H0:X⎯⎯⎯=22,HA:X⎯⎯⎯≠22
B. H0:X⎯⎯⎯>22.49,HA:X⎯⎯⎯≤22.49
C. H0:X⎯⎯⎯=22,HA:X⎯⎯⎯>22
D. H0:X⎯⎯⎯=22.49,HA:X⎯⎯⎯>22.49
E. H0:μ=22HA:μ>22
F. H0:μ=22,HA:μ≠22
G. H0:μ>22,HA:μ<22

Which I found to be D

And (d) Suppose the statistician decides to change the sample size to n=200 and regulate P(TypeI)=0.05. For what values of X⎯⎯⎯ should the null hypothesis in (a) be rejected?
A. Reject the null hypothesis if X⎯⎯⎯>22.29
B. Reject the null hypothesis if X⎯⎯⎯>22.00
C. Reject the null hypothesis if X⎯⎯⎯>22.50
D. Reject the null hypothesis if μ>22.50
E. Reject the null hypothesis if μ>22.29
F. Reject the null hypothesis if X⎯⎯⎯>22.49

Which I calculated was B. Im just not sure how to go about finding the probability of a type I error

I got an answer of .950 for the probabilty of a type I error. Which does not seem correct.

And I got .002 for part c)