# Chi-square test for independence

Chapter 15:

Chapter Exercises 15.18

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.

Credits Earned Very Uncertain 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

(a) State the null and alternative hypothesis in words.

Solution:

H0:

H1:

(b) The value of the test statistic is found to be xsquared=14.67. At a=0.01 , can it be concluded that the degree of certainty is independent of the credits earned? Why or why not? Explain! [Please note: You must show how you obtain the degrees of freedom, and the critical value of the test, and based on the critical value of the test do you reject and fail to reject the null hypothesis, and finally provide an interpretation of the result.]

Chapter Exercises 15.22

15.22 A student team examined parked cars in four different suburban shopping malls. One hundred vehicles were examined in each location. Research question:

Veh Type Somerset Oakland Great Lakes Jamestown Row Total

Car 44 49 36 64 193

Mini Van 21 15 18 13 67

Full SZ Van 2 3 3 3 10

SUV 19 27 26 12 84

Truck 14 6 17 9 46

Col Total 100 100 100 100 400

(a) State the null and alternative hypothesis, in words.

h0:

H1:

(b) The value of the test statistic is found to be Xsquared=24.53. At a=0.05, can it be concluded that the vehicle type vary by mall location? Why or why not? Explain! [Please note: You must show how you obtain the degrees of freedom, and the critical value of the test, and based on the critical value of the test do you reject and fail to reject the null hypothesis, and finally provide an interpretation of the result.]

Chapter Exercises 15.28

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. 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?

Perform a chi-square test for independence. (Data are from

Consumer Reports 56, no. 8 [August 1991], p. 519.)

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

(a) State the null and alternative hypothesis, in words.

H0:

H1:

(b) State the decision rule (a=0.05): (Region or regions under the sampling distribution of the test, where the null hypothesis will be rejected.) (Note: find the critical value of the test, and state your decision rule)

(c) Compute the X2 test statistic. [Please note: Either use technology, such as Excel/MegaStat, or do the hand computation. In any case you must copy/show your table of results and highlight the computed test statistic.]

(d) Make decision regarding the null hypothesis, and state your conclusion

#### Solution Summary

The solution provides step by step method for the calculation of test statistic for chi square test for independence. 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.