Question

A hospital director is told that 31% of the emergency room visitors are uninsured. The director wants to test the claim that the percentage of uninsured patients is below the expected percentage. A sample of 380 patients found that 95 were uninsured. Make the decision to reject or fail to reject the null hypothesis at the 0.02 level

A. Reject Null Hypothesis

or

B. Fail to Reject Null Hypothesis

Answer 1

Solution :

This is the left tailed test .

The null and alternative hypothesis is

H₀ : p = 0.31

H_a : p <0.31

$\hat p$ = x / n = 95/380=0.25

P₀ = 0.31

1 - P₀ = 1-0.31=0.69

Test statistic = z

= $\hat p$ - P₀ / [$\sqrt$P_{0 *} (1 - P₀ ) / n]

= 0.28-0.31/ [$\sqrt$(0.31*0.69) / 380]

= -1.26

P(z <-1.26) = 0.1038

P-value = 0.1038

$\alpha$ = 0.02

P-value >$\alpha$

Fail to Reject Null Hypothesis