# Chi-Square and GOF Tests

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 Preview

Please refer to the attachment for the solution.

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 ...

#### Solution Summary

The chi-square and GOF tests are determined.