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A hospital director is told that 47%47% of the treated patients are uninsured. The director wants...

A hospital director is told that 47%47% of the treated patients are uninsured. The director wants to test the claim that the percentage of uninsured patients is over the expected percentage. A sample of 350350 patients found that 175175 were uninsured. At the 0.010.01 level, is there enough evidence to support the director's claim?

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Answer #1

The following information is provided: The sample size is N = 350, the number of favorable cases is X = 175, and the sample proportion is pˉ ​= X/N = 175/350 = 0.5 and the significance level α = 0.01

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested

Ho:p ≤ 0.47

Ha:p > 0.47 ( claim )

(2) Rejection Region Based on the information provided, the significance level is a 0.01, and the critical value for a right-tailed test is ze2.33. The rejection region for this right-tailed test is R = {: z > 2.33) (3) Test Statistics The z-statistic is computed as follows 0.5-0.47 112 p-po VPol1-Po)/n V0.47(1 - 0.47)/350 (4) Decision about the null hypothesis Since it is observed that z1.125 2.33, it is then concluded that the null hypothesis is not rejected. Using the P-value approach: The p-value is p 0.1304, and since p 0.1304 0.01, it is concluded that the null hypothesis is not rejected( 5 )

Conclusion

It is concluded that the null hypothesis Ho is not rejected. Therefore, there is not enough evidence to support the director's claim  that the percentage of uninsured patients is over the expected percentage

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