Advanced Math Topics 12.4 Contingency Tables

Brown Eyes Blue Eyes Light Hair 10 33 Dark Hair 44 13 A contingency table is an arrangement of data into a two-way classification. One of the classifications is entered in rows and the other in columns. Brown Eyes Blue Eyes Light Hair 10 33 Dark Hair 44 13 The expected frequency of any cell is found by multiplying the total of its row by the total of its column and then dividing the result by the overall total.

Brown Eyes Blue Eyes Light Hair 10 33 Dark Hair 44 13 Total 43 57 1) Is eye color independent of hair color? Use a 5% level of significance. Brown Eyes Blue Eyes Light Hair 10 33 Dark Hair 44 13 Total 43 E = 43(54)/100 E = 43(46)/100 E = 23.22 E = 19.78 57 E = 57(54)/100 E = 57(46)/100 E = 30.78 E = 26.22 Total 54 46 100 (O – E)2 (10 – 23.33)2 Χ2 = Σ = = 7.527 E 23.22 Since our test statistic is larger, eye color is dependent on hair color. Do this for all four boxes and sum them up. Χ2 = 7.527 + 8.836 + 5.678 + 6.665 = 28.706 3.841 vs. The degrees of freedom is (# of rows – 1)(# of columns – 1). (2 – 1)(2 – 1) = 1

2.679 vs. 7.815. The ratings are independent of the course taken. From the HW: P. 621 2) A college uses student surveys to help decide to rehire professors. Students are asked to rate a professor. The college president wants to know if the rating of the course is independent of the course type. Use a 5% level of significance to help the president. Excellent Poor Fair Good Required Course 12 16 11 24 Elective 15 17 22 23 2.679 vs. 7.815. The ratings are independent of the course taken.

HW: P. 620 #2,3,5,7