Question

A hospital director is told that 54% of the treated patients are insured. The director wants to test the claim that the percentage of insured patients is less than the expected percentage. A sample of 260 patients found that 130 were insured. Find the value of the test statistic. Round your answer to two decimal places.

Answer 1

Solution :

The null and alternative hypothesis is

H₀ : p = 0.54

H_a : p 0.54

= x / n = 130 / 260 = 0.50

P₀ = 0.54

1 - P₀ = 1 - 0.54 = 0.46

Test statistic = z =

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.50 - 0.54 / [(0.54 * 0.46) / 260]

Test statistic = z = -1.29