Question

The research department of Coca Cola did a study to determine if there was a difference in the proportion of men who preferred Coke vs. women who preferred Coke. At the 10 significance level, is there a significant difference in the proportions of the preference for Coke between Men vs. Women? (Use z of -1.74) 75 out of 400 men preferred Coke over Pepsi. 25 out of 250 women preferred Coke over Pepsi. What is the p-value?

Answer 1

1 ) men eday PI x=75 ni= 400 women P2 X 2= 25 12= 250 a=0.lo Test that there is a difference in the proportion of men who preffered coke vs women who preffered coke Ho: P = P2 WS HI: PIEP2 p = Xi = 75 400 = 0.1875 Be = X2= 25 2 no 20 S.E= Pick-pi) + P2 (12) = 10.1875 (1-0.1875) + 0.1(1-0.1) 400 0.152344 +0.og 0.000381 +0.00036 -0.000741 400 S.E = 0.027219 250 = 0.0875 test statistic Zo= 8 -2 = 0,1875-0.1 0.027219 20=3,217 SE 0.027219 Pralie - P (Z1 > 1201) = P(IZ 13 13,211) -24 P(Z >3.21) Z ~ N(Oil) = 2 * ri- P(Z <3:21) = 2 x P) - 0.9993] = 2*0.0007 Prale=0.0014

Decision : Reject Ho if pralue <a ģ Here pucele = 0.0014 <2=0210 Reject Ho Conclusion There is sufficient evidence to support that there is difference in the proportions of men who preffered coke vs who proffered coke. coomen