Chi-Square and GOF Tests
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1.) A worker in an insurance company processes claims. The distribution of the number of claims processed each day in a week of this worker's life is as follows.
Day # of Claims
Monday 28
Tuesday 45
Wednesday 40
Thursday 23
Friday 29
The worker's boss thinks the worker's claims processing is sporadic and is not evenly distributed throughout the week. At the 0.05 level, is there sufficient evidence to conclude that the worker's claims processing is sporadic?
2.) Below is a compilation of student distribution in our four statistics classes from the summer of 2009.
Course: STAT 200 STAT 225 STAT 230 STAT 250
Percentage: 45.8 12.0 32.8 9.4
The enrollment report for the summer of 2011 is given as follows.
Course: STAT 200 STAT 225 STAT 230 STAT 250
Frequency: 249 71 133 47
At the 1% significance level, do the data provide sufficient evidence to conclude that 2011's enrollment distribution differs from the 2009 distribution?
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Solution Summary
The chi-square and GOF tests are determined.
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1.) A worker in an insurance company processes claims. The distribution of the number of claims processed each day in a week of this worker's life is as follows.
Day # of Claims
Monday 28
Tuesday 45
Wednesday 40
Thursday 23
Friday 29
The worker's boss thinks the worker's claims processing is sporadic and is not evenly distributed throughout the week. At the 0.05 level, is there sufficient evidence to conclude that the worker's claims processing is sporadic?
If by "sporadic" the worker's boss means "not evenly distributed" (as stated in the problem), then another way to ask this question is "do we have evidence that the proportion of claims processed by this worker on each of the 5 days of the week is significantly different from 20% for each day?" (Since "evenly distributed" would mean the same amount of work each day and with 5 work days in the week each day should account for 20% of the week's ...
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