Question

A hospital director is told that 55% 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 120 were insured. At the 0.05 level, is there enough evidence to support the director's claim?

Answer 1

Solution :

Given that,

= .55

1 - = 0.45

n = 240

x = 120

Level of significance = = 0.05

Point estimate = sample proportion = = x / n = 0.5

This a left (One) tailed test.

The null and alternative hypothesis is,

Ho: p = 0.55

Ha: p < 0.55

Test statistics

z = ( - ) / *(1-) / n

= ( 0.5 - 0.55) / (0.55*0.45) / 240

= -1.557

P-value = P(Z < z )

= P(Z < -1.557 )

= 0.0597

The p-value is p = 0.0597, and since p = 0.0597 > 0.05, it is concluded that the null hypothesis is fail to rejected.

Conclusion:

It is concluded that the null hypothesis Ho is fail to rejected. Therefore, there is not enough evidence to claim that the percentage of insured patients is less than the expected percentage at the α = 0.05 significance level.