Answer to Question #167562 in Statistics and Probability for kmy

Question

The percentage of physicians who are women is 27.9%. In a survey of physicians  employed by a large university health system, 60 of 142 randomly selected physicians  were women. Is there sufficient evidence at the 0.05 level of significance to conclude that  the proportion of women physicians at the university health system exceeds 27.9%?

a. State the hypothesis and identify the claim of the researcher.

b. Find the critical value(s). 

c. Compute the test value. 

d. Make a decision on the null hypothesis. 

e. Make a decision on the claim of the researcher.

Answer 1

Given,

n = 142

X = 60

α = 0.05

k = 0.279

(a) State the hypotheses and identify the claim

$H_0 : p ≤ 0.279$

$H_1 : p > 0.279 (\text{claim})$

(b) critical value is-

C.V. = +1.645 (right-tailed test with α = 0.05 )

(c) Compute the test value

$\hat{p} = X\\ p= \dfrac{60}{142}=0.422$

$q = 1− p = 1− 0.279 = 0.721$

$z = \dfrac{pˆ − p}{\sqrt{\frac{pq}{n}}}$

$=\dfrac{0.422 − 0.279}{\sqrt{\frac{(0.279)(0.721)}{142}}}$

$=3.8135$

(d) $H_o$ is rejected.

(e)  We don’t have sufficient evidence to support the claim.