Question 139052: Stanbon here are the other two that I needed to repost. I know it gets late there as I'm in another country, thanks for all of your help, your the best.
1. 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?
2. 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
A 8
B 8
C 9
D 11
E 14
Total 50
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 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.
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