Question

12.45 A random sample of 150 new car buyers who purchased Ford, General Motors (GM), and Chrysler models was selected, and their ages were recorded. The following table shows these data: Age Ford GM Chrysler 20-29 5 30-398 11 11 23 7 40-49 16 50-5924 15 5 15 10 0.05, perform a chi-square test to determine if the age of the buyer and the car brand he or she a. Using purchased are independent of one another. а 3 b. What conclusions can be made based on your results? c. Determine the p-value using Excel and interpret its meaning. d. Verify your results using PHStat

Answer 1

let us cosider H0 : age of the buyer and the car brand purchased Are independent of one another

and H1 : age of the buyer and the car brand purchased Are dependent of one another

using excel

Actual Values:
5 11 11
8 23 7
16 15 5
24 15 10

Expected Values:
9.54 11.52 5.94
13.4267 16.2133 8.36
12.72 15.36 7.92
17.3133 20.9067 10.78

Chi-Squared Values:
2.16054 0.0234722 4.31037
2.1933 2.8408 0.221244
0.845786 0.0084375 1.07657
2.58249 1.66878 0.0564378

Chi-Square = 17.9882

Degrees of Freedom = 6

p = 0.00626167

a ) chi square = 17.9882

b ) chi square table value at 0.05 with 6 degree of freedom is 12.591

since calculated value is greater than 12.591 so we reject H0 and conclude age of the buyer and the car brand purchased Are dependent of one another.

c ) p value is 0.0063 which is less than 0.05 so we reject H0 .

we have 95% evidence that age of the buyer and the car brand purchased Are dependent of one another.