Question 188237: I have tried every thing I know how. Can someone help me?
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? (Data are from Detroit Free Press, August 19, 2000, p. 8A.)
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.
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sample proportion = 205/226 =
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In Detroit, Michigan, only 151 of 296 buses passed the inspection.
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sample proportion = 151/296 =
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(a) State the hypotheses for a right-tailed test.
Ho: p(utica) - p(detroit) = 0
Ha; p(utica) - p(detroit) > 0
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(b) Obtain a test statistic and p-value.
I ran a 2-PropZTest on a TI calculator and got the following:
test statistic = z = 9.6491
p-value: 2.5243x10^-22
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(c) Is normality assured?
I'll leave that to you
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(d) If significant, is the difference also large enough to be important?
The test provides very strong evidence that the two proportions are not
equal. It is large enough to be important. Utica needs to take some
action or Detroit need to beef up its inspection criteria..
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Cheers,
Stan H.
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