Question

Use a χ² test to test the claim that in the given contingency table, the row variable and the column variable are independent.

160 students who were majoring in either math or English were asked a test question, and the researcher recorded whether they answered the question correctly. The sample results are given below. At the 0.10 significance level, test the claim that response and major are independent.

a. test statistic

b. critical value

Answer 1

solution - 160 students who were majoring or English were asked a test question, cher recorded whether they answered correctly. Then 2x2 contingency table below. in either maith and the reaser- the question math English Total correct a=27 6=43 ate=70 Incorrect b=53 d=37 brel=go Total atb= 80 Cid = 80 N=160 I I The null and alternative hypothesis is Ho the attributes, response and major are independent. I two us two Hi The attributes, response and major are dependent. Here we have to use chi-square (2x2) contingency table. test of independency for Then test statistics becomes, x² = x², die M (ad-bc) 2 Catb) (a+c) (Ctd) (btd) 2² = 160 [(27) (37) - (53) (43)] (80) (70) (80) (go) - 160 ( 1638400) 40320000 12² = 6.sols e x²cal = 6.5015

Critical value is, x² df = 7² dif at a= 0.10 level of significance. Xerilicy - 2.706 Here xial > Xenitical Then we reject the null hypothesis the He conclude that are dependent. two attributes, response and major