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 150 patients found that 70 were insured. Is there sufficient evidence at the 0.05 level to support the director's claim? State the alternative and null hypotheses.

Answer 1

Solution :

This is one tailed test .

The null and alternative hypothesis is

H0 : p = 0.54

Ha : p < 0.54

= x / n = 70 / 150 = 0.4667

1 - P0 = 0.46

Test statistic = z

= - P0 / [P0 * (1 - P0 ) / n]

= 0.4667 - 0.54 / [(0.54 * 0.46) / 150]

= -1.80

P(z < -1.80) = 0.0359

P-value = 0.0359

= 0.05

P-value <

Reject the null hypothesis .

There is sufficient evidence to support the directors claim.