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# Using Statistics to Conclude is Performance is Independent of Time of Shift

Suppose that the medical staff indicates that the results of a given laboratory procedure must be available 30 minutes after the physician submits a request for the service. In this situation, if the results arrived 30 minutes or less after the request, we regard the performance of the laboratory as timely. If results arrived more than 30 minutes after the request, we regard the performance as tardy. Focusing on the day, evening, and night shifts, suppose that we selected a random sample and obtained the following results:

Shift
Performance Day Evening Night
Timely 100 80 40
Tardy 20 30 40

If 0.05, use these results to test the proposition that the performance of the laboratory is independent of shift. After finding standard deviation and mean, give a brief analysis of the description of the data set.

#### Solution Preview

First, we build the cross tab on the left by figuring out the total in rows and columns.
Ho (null hypothesis): the performance of the laboratory is independent of shift.
Ha (alternative hypothesis): the performance of the laboratory is ...

#### Solution Summary

The expert uses statistics to conclude performance for independent of time of shifts are determined.

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