Question

A hospital director is told that 55% of the treated patients are insured. The director wants to test the claim that the percentage of insured patients is under the expected percentage. A sample of 180 patients found that 90 were insured. Make the decision to reject or fail to reject the null hypothesis at the 0.05 level.

Answer 1

Solution :

This is the left tailed test .

The null and alternative hypothesis is

H₀ : p = 0.55

H_a : p < 0.55

= x / n = 90 / 180 = 0.5

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.5 - 0.55 / [(0.55 * 0.45) / 180]

= -1.348

P-value = 0.0888

= 0.05

P-value >

Fail to reject the null hypothesis .