Question

A psychologist wants to see if a certain company has fair hiring practices in an industry where 60% of the workers are men and 40% are women. She finds that the company has 55 women and 52 men. Test to see if these numbers are different from the industry numbers, and if so, how are they different? Use alpha -.05 and four steps. A) what is the null hypothesis? B) what is the alternative hypothesis? C) what is the critical value of the test statistic? D) what is the value of the test statistic? E) Reject or accept the null? And why?

Answer 1

A)
`H_(0)`: p=0.5 (At least half of the workers are women,fair)

B)
`H_(a)`: p<0.5 (Less than half of the workers are women,unfair)

C) critical value of the test statistic is 1.64 (one tailed)

D) Test statistic is ≈ 0.29

E) Since 0.29<1.64, we fail to reject the null hypothesis. There is no significant evidence that the company has unfair hiring practices at 0.05 significance level.

Explanation:

Let p be the proportion of women workers in the company. Null and alternative hypotheses are

`H_(0)`: p=0.5 (At least half of the workers are women,fair)

`H_(a)`: p<0.5 (Less than half of the workers are women,unfair)

Test statistic can be found using the equation:

z=
`\frac{p(s)-p}{\sqrt{(p*(1-p))/(N) } }` where

• p(s) is the sample proportion of women workers (
  `(55)/(107) =0.514`)

• p is the proportion assumed under null hypothesis. (0.5)

• N is the sample size (55+52=107)

Then z=
`\frac{0.514-0.5}{\sqrt{(0.5*0.5)/(107) } }` ≈ 0.29

For alpha 0.05, critical value of the test statistic is 1.64 (one tailed)

Since 0.29<1.64, we fail to reject the null hypothesis. There is no significant evidence that the company has unfair hiring practices at 0.05 significance level.