Question

Recently, a large academic medical center determined that 10 of 24 employees in a particular position were male​, whereas 44​% of the employees for this position in the general workforce were male. At the 0.05 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?

What are the correct hypotheses to test to determine

Calculate the test statistic.

Identify the​ p-value from your technology​ output, rounding to three decimal places.

Answer 1

p: Proportion of male employees for a particular position

Null hypothesis : H_o : p=0.44

Alternate Hypothesis H_a ; p0.44

Two Tailed test:

Number of employees in particular position : n=24

Number of male employees in the particular position : x=10

Sample proportion of male employees in that particular position : = 10/24 =  0.4167

Hypothesize proportion :p_o = 0.44

Test Statistic = -0.23

For Two tailed test :

P(Z<-0.23) = 0.409

p-value = 2 x 0.409 = 0.818

p-value = 0.818

As P-Value i.e. is greater than Level of significance i.e (P-value:0.818 > 0.05:Level of significance); Fail to Reject Null Hypothesis

There is not sufficient evidence to conclude that the  proportion of males in this position at this medical center is different from what would be expected in the general ​workforce