Respuesta :
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
[tex]H_{0}: p = 0.50\\H_A: p < 0.50[/tex]
This is a one-tailed test.
Formula:
[tex]\hat{p} = \dfrac{x}{n} = \dfrac{118}{400} = 0.45[/tex]
[tex]z = \dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}[/tex]
Putting the values, we get,
[tex]z = \displaystyle\frac{0.45-0.50}{\sqrt{\frac{0.50(1-0.50)}{400}}} = -2[/tex]
Now, we calculate the critical value.
Now, [tex]z_{critical} \text{ at 0.05 level of significance } = -1.645[/tex]
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.
z statistic is less than the critical value therefore, the null hypothesis is rejected and the alternate hypothesis is accepted.
Given :
- 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.
Given that the sample size is, n = 400, p = 50% = 0.5, [tex]\alpha[/tex] = 0.05 and the number of women is, x = 180.
Now, the null and the alternate hypothesis is given by:
[tex]\rm H_0 ; p = 0.50[/tex]
[tex]\rm H_1 ; p < 0.50[/tex]
Now, use the below formula to find the value of [tex]z_{critical}[/tex]:
[tex]\widehat{p}=\dfrac{x}{n}=\dfrac{180}{400}=0.45[/tex]
[tex]z = \dfrac{\widehat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}} }[/tex]
Now, put the values of known terms in the above equation.
[tex]z =\dfrac{0.45-0.50}{\sqrt{\dfrac{0.5(1-0.5)}{400}} }[/tex]
z = -2
Now, [tex]z_{critical}[/tex] at 0.05 level of significance = -1.645
z statistic is less than the critical value therefore, the null hypothesis is rejected.
For more information, refer to the link given below:
https://brainly.com/question/11034287
