Question

A hospital director is told that 44% of the emergency room visitors are uninsured. The director wants to test the claim that the percentage of uninsured patients is above the expected percentage. A sample of 360 patients found that 180 were uninsured. At the 0.02 level, is there enough evidence to support the director's claim? Step 2 of 6 : Find the value of the test statistic. Round your answer to two decimal places.

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is

H₀ : p = 0.44

H_a : p > 0.44

= x / n = 180 / 360 = 0.50

P₀ = 0.44

1 - P₀ = 0.56

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.50 - 0.44/ [(0.44 * 0.56) / 360]

= 2.29

P(z > 2.29) = 1 - P(z < 2.29) = 0.011

P-value = 0.011

= 0.02

P-value <

Reject the null hypothesis .