Question

A professional employee in a large corporation receives an average of μ = 44.1 e-mails per day. Most of these e-mails are from other employees in the company. Because of the large number of e-mails, employees find themselves distracted and are unable to concentrate when they return to their tasks. In an effort to reduce distraction caused by such interruptions, one company established a priority list that all employees were to use before sending an e-mail. One month after the new priority list was put into place, a random sample of 33 employees showed that they were receiving an average of x = 35.8 e-mails per day. The computer server through which the e-mails are routed showed that σ = 15.1 Has the new policy had any effect? Use a 1% level of significance to test the claim that there has been a change (either way) in the average number of e-mails received per day per employee. What is the level of significance?

Group of answer choices

α = 0.99

α = 0.01

α = 0.03

α = 0.98

α = 0.02

Answer 1

Given that, sample size (n) = 33, sample mean = 35.8 emails

and population standard deviation = 15.1

The null and alternative hypotheses are,

H0 : μ = 44.1

Ha : μ ≠ 44.1

This hypothesis test is a two-tailed test.

Level of significance = α = 0.01

Test statistic is,

=> Test statistic = Z = -3.16

p-value = 2 * P(Z < -3.16) = 2 * 0.0008 = 0.0016

=> p-value = 0.0016

Since, p-value is less than α = 0.01, we reject the null hypothesis (H0).

Conclusion : There is sufficient evidence to support the claim that there has been a change (either way) in the average number of e-mails received per day per employee.