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# Chi square test for association

1) Sixty-four students in an introductory college economics class were asked how many credits they had earned in college, and how certain they were about their choice of major.

At &#945; = .01, is the degree of certainty independent of credits earned?

Data to construct the contingency table are below.

0-9 Credits Earned 10-59 Credits Earned
Very Uncertain: 12 Very Uncertain: 8
Somewhat Certain: 8 Somewhat Certain: 4
Very Certain: 3 Very Certain: 10

50 or More Credits Earned
Very Uncertain: 1
Somewhat Certain: 11
Very Certain: 7

2) A student team examined parked cars in four different suburban shopping malls. One hundred vehicles were examined in each location.

At &#945; = .05, does vehicle type vary by mall location?

Data to construct the contingency table are below.

Car Minivan
Somerset: 63 Somerset: 21
Oakland: 49 Oakland: 15
Great Lakes: 44 Great Lakes: 18
Jamestown: 46 Jamestown: 13

Full-sized Van SUV
Somerset: 2 Somerset: 27
Oakland: 3 Oakland: 19
Great Lakes: 3 Great Lakes: 26
Jamestown: 2 Jamestown: 12

Truck
Somerset: 14
Oakland: 6
Great Lakes: 17
Jamestown: 9

3) High levels of cockpit noise in an aircraft can damage the hearing of pilots who are exposed to this hazard for many hours. A Boeing 727 co-pilot collected 61 noise observations using a hand-held sound meter. Noise level is defined as "Low" (under 88 decibels), "Medium" (88 to 91 decibels), or "High" (92 decibels or more). There are three flight phases (Climb, Cruise, Descent).

At &#945; = .05, is the cockpit noise level independent of flight phase?

Data to construct the contingency table are below.

Low Noise Level Medium Noise Level High Noise Level
Climb: 6 Climb: 18 Climb: 1
Cruise: 6 Cruise: 8 Cruise: 13
Descent: 2 Descent: 3 Descent: 14

4) Can people really identify their favorite brand of cola? Volunteers tasted Coca-Cola Classic, Pepsi, Diet Coke, and Diet Pepsi, with the results shown below.

At &#945; = .05, is the correctness of the prediction different for the two types of cola drinkers? Could you identify your favorite brand in this kind of test? Since it is a 2 x 2 table, try also a two-tailed two-sample z test for &#960;1 =
&#960;2 and verify that z2 is the same as your chi-square statistic.

Which test do you prefer? Why?

Data to construct the contingency table are below.

Yes, got it right No, got it wrong
Regular Cola: 7 Regular Cola: 12
Diet Cola: 20 Diet Cola: 7

#### Solution Summary

The solution provides step by step method for the calculation of chi square test for association. Formula for the calculation and Interpretations of the results are also included. Interactive excel sheet is included. The user can edit the inputs and obtain the complete results for a new set of data.

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