Question

In: Statistics and Probability

A hospital director is told that 32% of the treated patients are uninsured. The director wants...

A hospital director is told that 32% of the treated patients are uninsured. The director wants to test the claim that the percentage of uninsured patients is below the expected percentage. A sample of 160 patients found that 40 were uninsured. At the 0.05 level, is there enough evidence to support the director's claim?

Solutions

Expert Solution

Solution :

Given that,

= 0.32

1 - = 0.68

n = 160

x = 40

Level of significance = = 0.05

Point estimate = sample proportion = = x / n = 0.25

This a right (One) tailed test.

Ho: p = 0.32

Ha: p < 0.32

Test statistics

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

= ( 0.25 - 0.32) / (0.32*0.68) / 160

= -1.90

P-value = P(Z<z)

= P(Z < -1.90)

= 0.0287

The p-value is p = 0.0287, and since p = 0.0287 < 0.05, it is concluded that the null hypothesis is rejected.

Conclusion:

It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the percentage of

uninsured patients is below the expected percentage 32%, at the 0.05 level of significance.

orchestra answered 2 years ago
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