The young bank manager in the last example 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 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 is 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
She tests the null hypothesis:
and decides to use 
. She finds:
m = 291.8
tu = 267.3
w = 277.6
th = 259.1
and the grand mean, = 274.3
She computes variance within:
[(276-291.8)2+(323-291.8)2+...+(243-267.6)2+...+(288-277.6)2+...+(254-259.1)2]/[34-4]=15887.6/30=529.6
Then she computes variance between:
[9(291.8-274.3)2+9(267.3-274.3)2+8(277.6-274.3)2+8(259.1-274.3)2]/[4-1] = 5151.8/3 = 1717.3
She computes her F-score:
Consulting the F-tables for 
and 3, 30 df, she finds that the
critical F-value is 2.92. Because her F-score is larger than the critical F-value, she concludes that the mean number of transactions is not the equal on different days of the week. She will
want to adjust her staffing so that she has more tellers on some days than on others.
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