# Z-Tests and T-Tests and Calculating Right-Tail P-Value

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 alpha = .025 (See story.news.yahoo.com accessed June 25, 2004.)

An auditor reviewed 25 oral surgery insurance claims from a particular surgical office, determining that the mean out-of-pocket patient billing above the reimbursed amount was $275.66 with a standard deviation of $78.11. (a) At the 5 percent level of significance, does this sample prove a violation of the guideline that the average patient should pay no more than $250 out-of-pocket? State your hypotheses and decision rule. (b) Is this a close decision?

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#### Solution Preview

Problem 3: 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?

Refer to attachment for formatting.

The null hypothesis tested is

H0: Population proportion=0.950

H1: Population proportion >0.950

The test statistic used is

(see attached)

Decision rule : ...

#### Solution Summary

This solution explains the Z-test of Hypothesis for the Proportion and t-test for Hypothesis of the Mean. Step by step detailed solutions are provided for the calculation of right-tail p-value/p- value.