The young bank manager in is still struggling with finding the best way to staff

Question

The young bank manager in is still struggling with finding the best way to staff her branch. She knows that she needs to have more tellers on Fridays than on other days, but she is trying to find if the need for tellers is constant across the rest of the week. She collects data for the number of transactions each day for two months. Here are her data:

Mondays: 276, 323, 298, 256, 277, 309, 312, 265, 311

Tuesdays: 243, 279, 301, 285, 274, 243, 228, 298, 255

Wednesdays: 288, 292, 310, 267, 243, 293, 255, 273

Thursdays: 254, 279, 241, 227, 278, 276, 256, 262

and she decides to use – .05.

Explanation / Answer

Here we need to compare more than two population means so one way ANOVA will be used. Hypotheses are:

H0: All the population means are equal.

Ha: At least one populaiton mean is different.

Following is the output of ANOVA analysis generated by excel:

The F test statistics is

F = 3.243

P-value: 0.0357

Since p-value is less than 0.05 so we reject the null hypothesis.

That is we cannot conclude that the need for tellers is constant across the rest of the week.

Anova: Single Factor SUMMARY Groups Count Sum Average Variance Mondays 9 2627 291.8889 569.1111 Tuesdays 9 2406 267.3333 681.25 Wednesdays 8 2221 277.625 491.9821 Thursdays 8 2073 259.125 348.6964 ANOVA Source of Variation SS df MS F P-value F crit Between Groups 5151.802 3 1717.267 3.242648 0.035735 2.922277 Within Groups 15887.64 30 529.588 Total 21039.44 33

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