On Saturday morning, Jennifer Bentford received a call at her home from the production supervisor at Bentford Electronics Plant 1. The supervisor indicated that she and the supervisors from Plants 2, 3, and 4 had agreed that something must be done to improve company morale and, thereby, increase the production output of their plants. Jennifer Bentford, president of Bentford Electronics, agreed to set up a Monday morning meeting with the supervisors to see if they could arrive at a plan for accomplishing these objectives.
By Monday each supervisor had compiled a list of several ideas, including a 4-day work week and interplant competition of various kinds.
After listening to the discussion for some time, Jennifer Bent-ford asked if anyone knew if there was a difference in average daily output for the four plants. When she heard no positive response, she told the supervisors to select a random sample of daily production reports from each plant and test whether there was a difference. They were to meet again on Wednesday afternoon with test results.
By Wednesday morning, the supervisors had collected the following data on units produced:

The supervisors had little trouble collecting the data, but they were at a loss about how to determine whether there was a difference in the output of the four plants. Jerry Gibson, the company€™s research analyst, told the supervisors that there were statistical procedures that could be used to test hypotheses regarding multiple samples if the daily output was distributed in a bell shape (normal distribution) at each plant. The supervisors expressed dismay because no one thought his or her output was normally distributed. Jerry Gibson indicated that there were techniques that did not require the normality assumption, but he did not know what they were.
The meeting with Jennifer Bentford was scheduled to begin in 3 hours, so he needed some statistical-analysis help immediately.

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Plant 1 Plant 2 Plant 3 Plant 4 4.306 853 .70 1704 2.852 948 2.705 2.320 1,900 2,702 2.72 4.150 4,711 4,0 2.900 3,300 2.933 3.950 . 3.200 3.627 2.300 2.802,975