Question

A hospital director is told that 28% 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 380 patients found that 95 were uninsured. Determine the decision rule for rejecting the null hypothesis, H0, at the 0.02 level.

Reject H0 if z_______

Answer 1

Solution :

Given that,

This is the two tailed test .

The null and alternative hypothesis is

H₀ : p = 0.28

H_a : p < 0.28

n = 380

x = 95

= x / n = 95 / 380 = 0.25

P₀ = 0.28

1 - P₀ = 1 - 0.28 = 0.72

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.25 - 0.28 / [0.28*0.72 /380 ]

= -1.302

Test statistic = z = - 1.302

P-value = 0.0964

= 0.02

P-value ≥

0.0964 ≥ 0.02

Do not Reject the null hypothesis .

There is insufficient evidence to suggest that