Chi Square and Anova
This exercise has the following two tasks:
Task 1: Consider the three samples listed in the table:
Inferences from Two Samples
Column A: 1,3,5
Column B: 0,6,2,5,2
Column C: 3,12,6,3
A B C
1 0 3
3 6 12
5 2 6
5 3
2
Obtain the sample mean and the sample standard deviation of each of the three samples.
– Obtain total sum of squares (SST,) treatment sum of squares (SSTR,) and error sum of
squares (SSE) by using the de?ning formulas and verify that the one-way ANOVA identity holds.
– Obtain SST, SSTR, and SSE by using the computing formulas.
– Construct the one-way ANOVA table.
Task 2: Read the case study titled Losses to Robbery and answer the corresponding
questions:
Losses to Robbery: The Federal Bureau of Investigation conducts surveys to obtain
information on the value of losses from various types of robberies. The results of the
surveys are published in Population-at-Risk Rates and Selected Crime Indicators.
Independent simple random samples of reports for three types of robberieshighway, gas
station, and convenience storegave the following data, in dollars, on the value of losses.
Highway Gas Station Convenience Store
952 1298 844
996 1195 921
839 1174 880
Inferences from Two Samples
Highway Gas Station Convenience Store
1088 1113 706
1024 953 602
1280 614
What does treatment mean square (MSTR) measure?
What does error mean square (MSE) measure?
Suppose that you want to perform a one-way ANOVA to compare the mean losses among the
three types of robberies. What conditions are necessary? How crucial are those conditions?
