Question

A hospital director is told that 54%54% of the emergency room visitors are insured. The director wants to test the claim that the percentage of insured patients is not the expected percentage. A sample of 260260 patients found that 130130 were insured. At the 0.050.05 level, is there enough evidence to support the director's claim?

Step 5 of 7:

Identify the value of the level of significance.

Answer 1

Given that, n = 260 and x = 130

=> sample proportion = 130/260 = 0.5

The null and alternative hypotheses are,

H0 : p = 0.54

Ha : p ≠ 0.54

Test statistic is,

=> Test statistic = -1.29

p-value = 2 * P(Z < -1.29) = 2 * 0.0985 = 0.1970

=> p-value = 0.1970

Step 5) The value of the level of significance = 0.05

Since, p-value is greater than 0.05 le level of significance, we fail to reject the null hypothesis (H0).