Question

Five hundred randomly selected automobile owners were questioned on the main reason they had purchased their current automobile. The results are given below.

	Styling	Engineering	Fuel Economy	Total
Male	70	130	150	350
Female	30	20	100	150
Total	100	150	250	500

a.	State the null and alternative hypotheses for a contingency table test.
b.	State the decision rule for the critical value approach. Let alpha = .01.
c.	Calculate the x2 test statistic.
d.	Give your conclusion for this test.

Answer 1

a) Hypothesis Ho. Tieo variables gender and purchasing automobile are independent HA! Two variables gender and purchasing automobile are depeodeot b) Decision rule At 220,01 significance level the critical value is, x²a, gr-1664) We reject to if X?> a, (7-0766-1) c) Observed frequencies (0;) Total Styling Engineering fuel economy 70 130 ISO 3 so Male (female Total 30 2o 150 Too aso 10.0 150 Soo

Now we calculate expected frequencies as, Eija AiXB N where Ai is sum of ith row, Bj is sum of with column and Nis sum of all frequencies Expected frequencies (E) Fuel Styling Engineering Engineering economy Male Female 70 30 175 7S 45 oij Eij Coij- E;;) Eij 70 70 30 30 los 175 roo 75 Soo Soo 5.9523 130 45 13. 8889 150 3,5714 8.3333 31.7459 Total Test statistic 7² = I Coij- f;;)? = 31,7459 Ei Critical value X a, 60-100cv Kiely (2-1) (3-1) C: rano. of rows K 20.01, 2 cano, of columns) = 9.210 2² >7²a a, cr-12cc-42 Hence rejest Ho conclusion : Two variables gender and purchasing automobile ore dependent. =