SOLUTION: First time asker-looking for help with the solution to this problem-just don't feel comfortable with the answer I'm getting. Help would be appreciated. In Utica, Michigan, 205

Question 138186: First time asker-looking for help with the solution to this problem-just don't feel comfortable with the answer I'm getting. Help would be appreciated.
In Utica, Michigan, 205 of 226 school buses passed the annual safety inspection. In Detroit, Michigan, only 151 of 296 buses passed the inspection. (a) State the hypotheses for a right-tailed test. (b) Obtain a test statistic and p-value. (c) Is normality assured? (d) If significant, is the difference also large enough to be important?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
In Utica, Michigan, 205 of 226 school buses passed the annual safety inspection.
p-hat(U)= 205/226 = 0.9071
In Detroit, Michigan, only 151 of 296 buses passed the inspection.
p-hat(D)=151/296 = 0.51
(a) State the hypotheses for a right-tailed test.
Comment: I'm assuming the claim is that the Utica proportion is greater
than the Detroit proportion.
Ho: P-hat(U)-P-hat(D) = 0
Ha: P-hat(U)-P-hat(D) >0
-------------------------------------
(b) Obtain a test statistic and p-value.
z(0.9071-0.51) = (0.3971-0)/sqrt[0.9071*0.0929/226 +0.51*0.49/296]= 11.3823
p-value = 2.63 x 10^-30 or practically speaking, zero
----------------

(c) Is normality assured?
Were buses randomly selected?
Samples should not exceed 10% of the population.
Data from the two samples should be independent.
-----------------------------------------

(d) If significant, is the difference also large enough to be important?
The evidence is overwhelming in support of rejecting Ho.
-----------------
Cheers,
Stan H.
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