Question

​Recently, a large academic medical center determined that 11 of 17 employees in a particular position were male​, whereas 41​% of the employees for this position in the general workforce were male. At the 0.01 level of​ significance, is there evidence that the proportion of males in this position at this medical center is different from what would be expected in the general​ workforce?

a. What are the correct hypotheses to test to determine if the proportion is​ different?

b. Calculate the test statistic.

c. What is the p-value?

d. State the conclusion of the test.

Answer 1

Step 1:

Ho: p = 0.41

Ha: p $\neq$ 0.41

Null hypothesis states that the proportion of males in this position at this medical center is 0.41 (same as population)

ALternative hypothesis states that the proportion of males in this position at this medical center is not equal to 0.41 (same as population)

Step 2:

x = 11

n = 17

2= T – np np(1-P) 11 – 17 * 0.41 17 * 0.41(1 -0.41) 1.987

p value = P(z > 1.987) = 2 (0.0233) = 0.0466

Step 3:

z critical for 0.01 level of significance = +/- 2.58

As z stat ( 1.987) does not fall in the rejection area, we fail to reject the Null hyopothesis.

Also as the p value (0.0466) is greater than level of significance (0.01),  we fail to reject the Null hyopothesis.

Hence we do not have sufficient evidence to believe that the proportion of males in this position at this medical center is not equal to 0.41 at 0.01 level of significance.