Mathematics, 14.04.2020 19:55 gearchanger52p02zf8

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?

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Answer from: makiahlynn3642

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.

Answer from: Quest

Letter a i would say
In the diagram below, ab is parallel to cd. what is the value y? a.150b.50c.60d.30

Answer from: Quest

$a_1 = 1$ , and

$a_{n+1} = a_n + (n + 1)$ for $n \ge 1$

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote $a_1 = 1$ , $a_2 = 3$ , $a_3 = 6$ , so that we can call

1 the 1st term, 3 the 2nd term, 6 the 3rd term,etc.

note the following:

from the 1st term (1) to the 2nd term (3), we go up by 2,from the 2nd term (3) to the 3rd term (6), we go up by 3from the 3rd term (6) to the 4th term (10), we go up by 4, andfrom the 4th term (10) to the 5th term (15), we go up by 5.

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from $a_1 = 1$ , to get to $a_2 = 3$ , we add $2(=1+1)$