Question 139052
I answered those this morning at 7:00 EST.
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2. 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.
Ho: p(Ut)-p(Dt)= 0
Ha: p(Ut)-p(Dt)>0
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(b) Obtain a test statistic and p-value.
p-hat(Ut) = 205/226= 0.9071;p-hat(Dt)=0.5101; p(pooled)=(431/522)=0.8257
z = (9071-0.5101)/[ 0.8257*0.1743/226 + 0.8257*0.1743/296]= 9.6491
p-value: 2.52x10^-22
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(c) Is normality assured? 
I'll let you check out those conditions.
They should be listed in your text.
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(d) If significant, is the difference also large enough to be important?
Since p-value is so small the difference is very significant.
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3. Prof. Green’s multiple-choice exam had 50 questions with the distribution of correct answers shown below. Research question: At α = .05, can you reject the hypothesis that Green’s exam answers came from a uniform population 
Correct Answer Frequency.......Expected
A ................8................10
B ................8................10
C ................9................10
D ...............11................10
E ...............14................10
Total 50 
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Ho: Observed Frequencies are equal
Ha; Observed Frequencies are not equal
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I ran a Chi-Sq Test on a 2x5 matrix with observed in the 1st row and expected in the 2nd row and got the following results:
Test statistic: Chi-Sq = 1.2114
p-value: 0.8762
Meaning: 87.6% of test results could have given stronger evidence for
rejecting Ho.
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Conclusion: Since p-value is greater than alpha=5%, Fail to reject Ho.
The grades follow a uniform distribution.
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Cheers,
Stan H.