Question

The percentage of physicians who are women is 27.9%. In a survey of physicians employed by a large

university health system, 45 of 120 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%?​

Answer 1

Explanation:

Given that the percentage of physicians who are women is 27.9%. In a survey of physicians employed by a large university health system,

45 of 120 randomly selected physicians were women.

Sample size n = 120

Sample proportion p =
`(45)/(120) \\=0.375`

H0: p = 0.279

Ha: p >0.279

(Two tailed test at 5% significance level)

p difference = 0.096

STd error of p assuming H0 true

=
`\sqrt{(pq)/(n) } \\=\sqrt{(0.279(0.721)/(120) } \\=0.041`

Test statistic Z =
`(0.096)/(0.041) \\=2.345`

Z critical value one tailed is 1.645

Since Z statistic > 1.645 we reject H0

There is evidence to conclude that the proportion of women physicians at the university health system exceeds

27.9%