Question

A hospital director is told that 35%35% of the treated patients are uninsured. The director wants to test the claim that the percentage of uninsured patients is under the expected percentage. A sample of 120120 patients found that 3030 were uninsured. Determine the decision rule for rejecting the null hypothesis, H0H0, at the 0.020.02 level.

Answer 1

The Critical Value: The critical value (Left tail) at = 0.02, Zcritical = -2.054

The Decision Rule:    

The Critical Value Method: If Zobserved is < -2.054, Then Reject H0.

The p value Method: If the P value is < (0.02), Then Reject H0

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The hypothesis test has been done below for your reference

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Left Tailed Test for 1 proportion:

Let = The sample proportion of treated patients who are uninsured = 30/120 = 0.25

Let p = The population proportion of treated patients who are uninsured = 0.35

1 - p = 0.65

= 0.02

The Hypothesis:

H0: p = 0.35: The population proportion of treated patients who are uninsured is equal to 0.35.

Ha: p < 0.35: The population proportion of treated patients who are uninsured is less than 0.35.

This is a left Tailed Test.

The Test Statistic:

Z observed = -2.30

The p Value:    The p value (Left Tail) for Z = -2.30, is; p value = 0.0107

The Critical Value: The critical value (Left tail) at = 0.02, Zcritical = -2.054

The Decision Rule:    

The Critical Value Method: If Zobserved is < -Zcritical, Then Reject H0.

The p value Method: If the P value is < , Then Reject H0

The Decision:   

The Critical Value Method: Since Z observed (-2.3) is < -2.054, We Reject H0

The p value Method: Since P value (0.0107) is < (0.02), We Reject H0.

The Conclusion: There is sufficient evidence at the 98% significance level to conclude that the population proportion of treated patients who are uninsured is less than 0.35.

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