Question

A hospital director is told that 54% of the emergency room visitors are insured. The director wants to test the claim that the percentage of insured patients is under the expected percentage. A sample of 140 patients found that 70 were insured. Determine the decision rule for rejecting the null hypothesis, H0, at the 0.05 level.

Reject H0 if

Answer 1

Solution :

This is the left tailed test .

The null and alternative hypothesis is

H₀ : p = 0.54

H_a : p < 0.54

= x / n = 70 / 140 = 0.50

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.50 - 0.54 / [(0.54 * 0.46) / 140]

= -0.95

P(z < -0.95) = 0.1711

P-value = 0.1711

= 0.05

P-value >

Fail to reject the null hypothesis .