# Five Step Procedure: Chi-Square Test

15.18 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. Research question: At α = .01, is the degree of certainty independent of credits earned? Show all five steps of hypothesis testing.

Credits Earned Very Uncertain Somewhat Certain Very Certain Row Total

0-9 12 8 3 23

10-59 8 4 10 22

60 or more 1 7 11 19

Col Total 21 19 24 64

15.22 A student team examined parked cars in four different suburban shopping malls. One hundred vehicles were examined in each location. Research question: At α = .05, does vehicle type vary by mall location? (Data are from a project by MBA students Steve Bennett, Alicia Morais, Steve Olson, and Greg Corda). Show all five steps of hypothesis testing.

Vehicle Type Somerset Oakland Great Lakes Jamestown Row Total

Car 44 49 36 64 193

Minivan 21 15 18 13 67

Full-sized Van 2 3 3 2 10

SUV 19 27 26 12 84

Truck 14 6 17 9 46

Col Total 100 100 100 100 400

15.24 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 handheld 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). Research question: At α = .05, is the cockpit noise level independent of flight phase? (Data are from Capt. Robert E. Hartl, retired). Show all five steps of hypothesis testing.

Noise Level Climb Cruise Descent Row Total

Low 6 2 6 14

Medium 18 3 8 29

High 1 3 14 18

Col Total 25 8 28 61

15.28 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. Research question: At α = .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 �- 2 table, try also a two-tailed two-sample z test for π1 = π2 (see Chapter 10) and verify that z2 is the same as your chi-square statistic. Which test do you prefer? Why? (Data are from Consumer Reports 56, no. 8 [August 1991], p. 519.) Show all five steps of hypothesis testing.

Correct? Regular Cola Diet Cola Row Total

Yes, got it right 7 7 14

No, got it wrong 12 20 32

Col Total 19 27 46

https://brainmass.com/statistics/chi-squared-test/five-step-procedure-chi-square-test-274111

#### 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. An interactive excel sheet is included. The user can edit the inputs and obtain the complete results for a new set of data.