Governmental Use of email. The Federal Government wants to determine if the mean number of business emails sent and received per business day by its employees differs from the mean number of emails sent and received per day by corporate employees, which is 101.5. Suppose the department electronically collects information on the number of business emails sent and received on a randomly selected business day over the past year from each of 10,163 randomly selected Federal employees. The results are provided in the file FedEmail . Test the Federal Government’s hypothesis at α = .01. Discuss the practical significance of the results.

Test whether the mean number of business emails sent and received per business day by its employees differs from the mean number of emails sent and received per day by corporate employees.

Explain the practical significance of the results.

Explanation of Solution

Calculation:

The hypotheses are given below:

Null hypothesis: H0:μ=101.5

Alternative hypothesis: Ha:μ≠101.5

Software Procedure:

Step-by-step procedure to find the sample mean, standard deviation and sample size using the Excel:

In the Excel sheet, enter Email Sent and Received in one column.
In Data, Select Data Analysis and Choose Descriptive Statistics.
In Input Range Select Email Sent and Received and Click Labels in First Row.
Select Summary Statistics.
Click Ok.

Output using the Excel is given below:

From the output, the sample mean value is 100.47, the sample standard deviation is 25, and the sample size is 10,163.

The formula for finding test statistic is as follows:

t=x¯−μ0sn

Here, x¯ represents the sample mean, μ0 represents the hypothesized value of the population mean, σ represents the population standard deviation, and n represents the sample size.

Substitute 100.47 for x¯, 25 for μ0, 25 for σ, and 10,163 for n in t formula.

t=100.47−101.52510,163=−1.0325100.8117=−1

Essentials Of Statistics For Busin...

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Essentials Of Statistics For Busin...

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