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A hospital director is told that 34% of the treated patients are uninsured. The director wants...

A hospital director is told that 34% of the treated patients are uninsured. The director wants to test the claim that the percentage of uninsured patients is less than the expected percentage. A sample of 140 patients found that 35 were uninsured. Determine the decision rule for rejecting the null hypothesis, H0, at the 0.02 level.

Math   Statistics-And-Probability   
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Answer #1

The following information is provided: The sample size is N = 140, the number of favorable cases is X = 35, and the significance level is α=0.02

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

Ho: p = 0.34

Ha: p < 0.34

This corresponds to a left-tailed test, for which a z-test for one population proportion needs to be used.

(2) Rejection Region

Based on the information provided, the significance level is α=0.02, and the critical value for a left-tailed test is z_c = -2.05

The rejection region for this left-tailed test is

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