Question

A hospital director is told that 79% 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 240 patients found that 180 were insured. Find the value of the test statistic. Round your answer to two decimal places.

Answer 1

Given that, n = 240 and x = 180

sample proportion $(\hat p)$ = x/n = 180/240 = 0.75

The null and the alternative hypotheses are,

$H_0: p = 0.79$

$H_a: p < 0.79$

Test statistic is,

$Z = \frac { \hat p - p}{\sqrt {\frac { p*(1-p)}{n}}}= \frac { 0.75 - 0.79}{\sqrt {\frac {0.79*(1-0.79)}{240}}}= -1.5214$

Test statistic is, z = -1.52