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Home » Introductory Business Statistics » F-test and one-way anova » A simple test: Do these two samples come from populations with the same variance?

An example

27 October, 2015 - 11:14
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A young banker has recently been promoted and made the manager of her own branch. After a few weeks, she has discovered that maintaining the correct number of tellers seems to be more difficult than it was when she was assistant manager of a larger branch. Some days, the lines are very long, and other days, the tellers seem to have little to do. She wonders if the number of customers at her new branch is simply more variable than the number of customers at the branch where she used to work. Because tellers work for a whole day or half a day (morning or afternoon), she collects the following data on the number of transactions in a half day from her branch and the branch where she used to work:

Her branch:156, 278, 134, 202, 236, 198, 187, 199, 143, 165, 223
Old branch: 345, 332, 309, 367, 388, 312, 355, 363, 381

She hypothesizes:

H_{0}=\sigma _{h}^{2}=\sigma _{o}^{2}

H_{a}=\sigma _{h}^{2}\neq \sigma _{h}^{2}

She decides to use \alpha=.05 . She computes the sample variances and finds:

sh2 =2027.1
so2 =795.2

Following the rule to put the larger variance in the numerator, so that she saves a step, she finds:

F=\frac{S_{h}^{2}}{S_{o}^{2}}=\frac{2027.1}{795.2}=2.55

From the table, (remembering to use the \alpha=.025 table because the table is one-tail and the test is two-tail) she finds that the critical F for 10,8 df is 4.30. Because her F-score is less than the critical score, she concludes that her F-score is "close to one", and that the variance of customers in her office is the same as it was in the old office. She will need to look further to solve her staffing problem.

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