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?

Solution: We need to test the following null and alternative hypotheses:

This corresponds to a right-tailed z-test for proportions. The significance level is set to. The critical value is computed as

We will reject the null hypothesis if. From the information provided we know that

The z-statistics is computed as

The right-tailed critical z-value for is given by

Since we have that >, then we reject the null hypothesis.

This means that we have enough evidence to support the claim that they are exceeding their goal, at the 0.025 significance level.

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