Question

The CEO of a software company is committed to expanding the proportion of highly qualified women in the organization’s staff of salespersons. He believes that the proportion of women in similar sales positions across the country in 2004 is less than 45%. Hoping to find support for his belief, he directs his assistant to collect a random sample of salespersons employed by his company, which is thought to be representative of sales staffs of competing organizations in the industry. The collected random sample of size 50 showed that only 18 were women.

State the appropriate null and alternative hypotheses in this situation.

Answer 1

Null Hypothesis,
`H_0` : p
`\geq` 45%

Alternate Hypothesis,
`H_A` : p < 45%

Explanation:

We are given that the proportion of women in similar sales positions across the country in 2004 is less than 45%.

The collected random sample of size 50 showed that only 18 were women.

Let p = proportion of women in similar sales positions across the country in 2004

So, Null Hypothesis,
`H_0` : p
`\geq` 45%

Alternate Hypothesis,
`H_A` : p < 45%

Here, null hypothesis states that the proportion of women in similar sales positions across the country in 2004 is more than or equal to 45%.

On the other hand, alternate hypothesis states that the proportion of women in similar sales positions across the country in 2004 is less than 45%.

The test statistics that would be used here is One-sample z proportion test statistics, i.e;

T.S. =
`\frac{\hat p -p}{\sqrt{(\hta p(1-\hat p))/(n) } }` ~ N(0,1)

Hence, the above hypothesis is appropriate for the given situation.