# Chapter 11: Chi-squared (χ2) tests of fit

Answers for Data Skill Challenges for every chapter in the book can be found to check your performance and widen your understanding.

1. RQ: Are any of the four gums chosen more often by focus group participants?

H0: There is no difference between observed and expected frequencies of gum preference.

H1: There is a difference between observed and expected frequencies of gum preference.

α = .05

χ2crit(3) = +7.815

χ2(3) = +10.17, p = .02 or χ2(3) = +10.17, p <.05

φC = 0.33

Conclusion: Reject the null and accept the alternative. The chi-squared is statistically significant. There is a difference between observed and expected frequencies of gum preference. Cramérs V is 0.33. Gum D is picked most often, while the other three gums are roughly the same.

2)      RQ: Are any of the logos chosen more often by the employees?

H0: There is no difference between observed and expected frequencies of logo preference.

H1: There is a difference between observed and expected frequencies of logo preference.

α = .05

χ2(2)crit = +5.991

χ2(2) = 3.75, p = .154 or χ2(2) = 3.75, p > .05

Conclusion: Retain the null. The chi-squared is not statistically significant. There is insufficient evidence that there is a difference between observed and expected frequencies of logo preference.

3)      RQ: Are there more accidents on night shift for some plants?

H0: Accidents by plant are independent of shift.

H1: Accidents by plant are not independent of shift.

α = .05

χ2crit(11) = +19.675

χ2(11) = +21.961, p = .03 or c2(11) = +21.961, p <.05

φC = 0.46

Conclusion: Reject the null and accept the alternative. The chi-squared is statistically significant. Accidents by plant are not independent of shift. Cramérs V is 0.46. Plants 9, 10 and 12 have noticeably higher accident rates on the night shift than wed expect by shift or plant alone.

4)      RQ: Are there more sales for food for some colour carts?

H0: Sales by food type are independent of cart colour.

H1: Sales by food type are not independent of cart colour.

α = .05

χ2(2)crit = 5.991

χ2(2) = 2.68, p = .26 or χ2(2) = 2.68, p > .05

Conclusion: Retain the null. The chi-squared is not statistically significant. There is insufficient evidence to conclude that sales by food type are not independent of cart colour.