Question

After being rejected for employment, Appa Love learns that the Old West Credit Company has hired only 6 women among the last 20 new employees. She also learns that the pool of applicants is very large, with an approximately equal number of qualified men as qualified women. Help her address the charge of gender discrimination by finding the probability of hiring 6 or fewer women when 20 people are hired, assuming that there is no discrimination based on gender. That is, address the claim that the proportion of females hired is 50%. Use the sample data stated above.

Determine the null and alternative hypotheses.

Answer 1

Null hypothesis,
`H_(o) : P = 0.50`

Alternative hypothesis,
`H_(a) : P \\eq 0.50`

Explanation:

The null hypothesis is the statement about a population that we want to reject with the sample data. It always shows that their is no significant relationship between the measured and observed variables.

The alternative hypothesis always disproves the null hypothesis, it claims that there is a significant relationship between the observed and measured data

Since the claim is that the proportion of females hired is 50% = 0.50 (null hypothesis), The alternative hypothesis claims that the proportion of females hired is not 0.5

Null hypothesis,
`H_(o) : P = 0.50`

Alternative hypothesis,
`H_(a) : P \\eq 0.50`

Answer 2

Null Hypothesis,
`H_0` : p = 50%

Alternate Hypothesis,
`H_A` : p
`\\eq` 50%

Explanation:

We are given that after being rejected for employment, Appa Love learns that the Old West Credit Company has hired only 6 women among the last 20 new employees.

We have to address the claim that the proportion of females hired is 50%.

Let p = proportion of females hired.

So, Null Hypothesis,
`H_0` : p = 50%

Alternate Hypothesis,
`H_A` : p
`\\eq` 50%

Here, null hypothesis states that the proportion of females hired is 50% and there is no discrimination based on gender.

On the other hand, alternate hypothesis states that the proportion of females hired is different from 50% and there is some discrimination based on gender.

So, this would be the appropriate hypothesis for conducting the test.