SOLUTION: 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 sam

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Question 177525: 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?
Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
H0 = 95% of orders filled
Ha = greater than 95% of orders filled
We'll use a z test for a proportion. The critical value for a one tailed alpha 0.025 test is z = 1.96. We'll reject the null hypothesis if our z test statistic is greater than that.
Find the test statistic z:
phat = 485/500 = 0.97
z = (phat-p)/sqrt(p*(1-p)/N)
z = (0.97-0.95)/sqrt(0.95*0.05/500)
z = 2.0519


This is greater than the z value from the table for a one tailed test, with alpha = 0.025 (z = 1.96), so we reject the null hypothesis. We can be reasonably sure that they are exceeding their goal.