Question

The board of directors of a corporation has agreed to allow the human resources manager to move to the next step in planning daycare service for employees' children if the manager can prove that at least 25% of the employees have interest in using the service. The HR manager polls 300 employees and 90 say they would seriously consider utilizing the service.
At the 0.10 level of significance, is there enough interest in the service to move to the next planning stage?

Answer 1

Answer:

Yes, at the 0.10 level of significance, there is enough interest in the service to move to the next planning stage.

Step-by-step explanation:

We are given that the board of directors of a corporation has agreed to allow the human resources manager to move to the next step in planning daycare service for employees' children if the manager can prove that at least 25% of the employees have interest in using the service.

The HR manager polls 300 employees and 90 say they would seriously consider utilizing the service.

Let p = population proportion of employees who seriously consider utilizing the service

SO, Null Hypothesis, $H_0$ : $p \geq$ 25%   {means that the service will move to the next planning stage}

Alternate Hypothesis, $H_a$ : p < 25%   {means that the service will not move to the next planning stage}

The test statistics that will be used here is One-sample z proportion test statistics because we don't know about the population standard deviation;

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

where,  $\hat p$ = sample proportion of employees who seriously consider

                   utilizing the service = $\frac{90}{300}$ = 0.30

             n = sample of employees = 300

So, test statistics  =  $\frac{0.30-0.25}{\sqrt{\frac{0.30(1-0.30)}{300} } }$  

                               =  1.889

Now at 0.10 significance level, the z table gives critical value of -1.2816 for left-tailed test. Since our test statistics is more than the critical value of z so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region.

Therefore, we conclude that there is enough interest in the service to move to the next planning stage.