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# Chi square test for independence of variables

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A production process uses five machines during each of two work shifts. The frequencies with which these machines need to be repaired are as follows:

Machine
Shift 1 2 3 4 5

1 12 6 12 14 6
2 23 4 9 16 5

Are the machine breakdowns independent of shift?

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https://brainmass.com/statistics/chi-squared-test/chi-square-test-independence-variables-18205

#### Solution Preview

See attached file

A production process uses five machines during each of two work shifts. The frequencies with which these machines need to be repaired are as follows:

Machine
Shift 1 2 3 4 5

1 12 6 12 14 6
2 23 4 9 16 5

Are the machine breakdowns independent of shift?

Answer: Yes , machine breakdowns are independent of shift
See calculations below:

We will have to do a chi squared test as a test of independence to check whether there is any relationship between breakdown and shift

The significance level at which this test is to be carried out has not been indicated so we will assume it to be 0.05

Null Hypothesis: H0: There is no relationship between breakdown and ...

#### Solution Summary

Performs a Chi square test for independence of variables.

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