# Test statistics

The data below represents fields of specialization for the randomly selected sample of undergraduate students. Test to determine whether there is a significant difference in the fields of specialization between regions of the country. Use a=.05

Northeast Midwest south west Total
Business 54 65 28 93 240
Engineering 15 24 8 33 80
LiberalArt 65 84 33 98 280
Fine ARt 13 15 7 25 60
Health 3 12 4 21 40

Totals 150 200 80 270 700

1. State the critical value of the chi-square random variable for this test of independence of catagories.
2. Calculate the value of the test statistic.
3. what is the conclusion for the test?

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#### Solution Preview

...s 21.03.
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<br>I will explain part 3 right now.
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<br>When you calculate the test statistic, you have to see what that value is. IF the value that you calculate is LESS then 21.03, then you have to conclude that there is NO RELATIONSHIP between the location and the program of study.
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<br>On the other hand, if you test statistic is HIGHER then 21.03, then you have to conclude that there IS A RELATIONSHIP between the location and the program of study.
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<br>2) to calculate the test stat.
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<br>Chi sq. is a test that compairs the actual ...