Question

Executives at a large multinational company are being accused of spending too much time on email and not enough time with their employees whom they supervise. In order to see if this is true, the VP of Human Resources decides to do a comparison of the number of minutes per day that the top 100 executives spend on e-mail compared to the total minutes spent by everyone in the company. The average minutes spent per day by each employee was 96 minutes. The average for just the top 100 executives was 91 minutes with a standard deviation of 25 minutes. On average, are the Executives spending more time on e-mail than all the employees? If you wanted to use the the 1% level of significance to test your hypothesis, what would be the correct critical value?

Answer 1

Answer:

We conclude that there is not enough evidence to support the claim that company is spending too much time on email.

Step-by-step explanation:

We are given the following in the question:  

Population mean, μ = 96 minutes

Sample mean, $\bar{x}$ = 91 minutes

Sample size, n = 100

Alpha, α = 0.05

Sample standard deviation, s = 25 minutes

First, we design the null and the alternate hypothesis

$H_{0}: \mu \leq 96\text{ minutes}\\H_A: \mu > 96\text{ minutes}$

We use one-tailed t test to perform this hypothesis.

Formula:

$t_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}} }$

Putting all the values, we have

$t_{stat} = \displaystyle\frac{91 - 96}{\frac{25}{\sqrt{100}} } = -2$

Now, $t_{critical} \text{ at 0.05 level of significance, 99 degree of freedom } = 1.6603$

Since,                        

The calculated test statistic is less than the critical value, we fail to reject the null hypothesis and accept it.

Thus, we conclude that there is not enough evidence to support the claim that company is spending too much time on email.