Question 138186
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
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(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
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(c) Is normality assured?
Were buses randomly selected?
Samples should not exceed 10% of the population.
Data from the two samples should be independent.
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(d) If significant, is the difference also large enough to be important? 
The evidence is overwhelming in support of rejecting Ho.
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Cheers,
Stan H.