Given `mu=5,sigma=.5,n=16,bar(x)=5.516` . We want to test the claim that `mu>5` at the 99% confidence level `(alpha=.01)` .

(1) `H_0:mu=5` `H_1:mu>5`

(2) Since `alpha=.01` the critical point is `z_(.01)=2.33`

(3) The test value is `z=(5.516-5)/(.5/sqrt(16))=4.128`

(4) The p-value is found in the standard normal table.(Try to find 4.128 in...

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Given `mu=5,sigma=.5,n=16,bar(x)=5.516` . We want to test the claim that `mu>5` at the 99% confidence level `(alpha=.01)` .

(1) `H_0:mu=5` `H_1:mu>5`

(2) Since `alpha=.01` the critical point is `z_(.01)=2.33`

(3) The test value is `z=(5.516-5)/(.5/sqrt(16))=4.128`

(4) The p-value is found in the standard normal table.(Try to find 4.128 in the table -- no z score goes that high. Usually there is a note for z<-3.5 and greater than 3.5) Since z>3.5, p=.0001 (My calculator gives me .0000183) Since `p<alpha` we reject the null hypothesis.

(5) There is sufficient evidence to claim with 99% certainty that `mu>5`