Question

Last year, 50% of MNM. Inc. employees were female. It is believed that there has been a reduction in the percentage of females in the company. This year, in a random sample of 400 employees. 180 were female. a. What are the null and the alternative hypotheses?b. At 95% confidence using the critical value approach, determine if there has been a significant reduction in the proportion of females.

Answer 1

Answer:

We conclude that there has been a significant reduction in the proportion of females.

Step-by-step explanation:

We are given the following in the question:

Sample size, n = 400

p = 50% = 0.5

Alpha, α = 0.05

Number of women, x = 118

First, we design the null and the alternate hypothesis  

$H_{0}: p = 0.50\\H_A: p < 0.50$

This is a one-tailed test.  

Formula:

$\hat{p} = \dfrac{x}{n} = \dfrac{118}{400} = 0.45$

$z = \dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}$

Putting the values, we get,

$z = \displaystyle\frac{0.45-0.50}{\sqrt{\frac{0.50(1-0.50)}{400}}} = -2$

Now, we calculate the critical value.

Now, $z_{critical} \text{ at 0.05 level of significance } = -1.645$

Since the calculated z-statistic is less than the critical value, we fail to accept the null hypothesis and reject it. We accept the alternate hypothesis.

Thus, there has been a significant reduction in the proportion of females.