Question 127724: The Web-based company Oh Baby! Gifts has a goal of processing 95 percent of its orders on the
same day they are received. If 485 out of the next 500 orders are processed on the same day, would
this prove that they are exceeding their goal, using α = .025? (See story.news.yahoo.com accessed
June 25, 2004.)
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! The Web-based company Oh Baby! Gifts has a goal of processing 95 percent of its orders on the same day they are received. If 485 out of the next 500 orders are processed on the same day, would this prove that they are exceeding their goal,
using α = .025?
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Ho: p = 0.95
Ha: p > 0.95
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one-tail z-test with critical value = 1.96;
alpha = 2.5%; p-hat=485/500=0.97
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Test Statistic:
z(0.97) = (0.97-0.95)/sqrt((0.95*0.05)/500)= 2.052
p-value = 0.0201
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Conclusion: Reject Ho because the test statistic > critical value; also
the p-value is < alpha.
There is significant statistical evidence that p is not 95%.
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Cheers,
Stan H.
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