Question

At a high school debate tournament, half of the teams were asked to wear suits and ties and the rest were asked to wear jeans and t-shirts. The results are given in the table below. Test the hypothesis at the 0.05 level that the proportion of wins is the same for teams wearing suits as for teams wearing jeans.

a. critical value

b. test statistic

Answer 1

Answer)

Ho : P 1 = P 2

Ha : P1 not equal to P2

P1 is for suits

P2 is for t shirt

N1 = 50, P1 = 22/50

N2 = 50, P2 = 28/50

First we need to check the conditions of normality that is if n1p1 and n1*(1-p1) and n2*p2 and n2*(1-p2) all are greater than equal to 5 or not

N1*p1 = 22

N1*(1-p1) = 28

N2*p2 = 28

N2*(1-p2) = 22

All the conditions are met so we can use standard normal z table to conduct the test

Test statistics z = (P1-P2)/standard error

Standard error = √{p*(1-p)}*√{(1/n1)+(1/n2)}

P = pooled proportion = [(p1*n1)+(p2*n2)]/[n1+n2]

After substitution

Test statistics z = -1.2

To find critical value first we need to divide the alpha (0.05) into two parts

As our test is two tailed

0.05/2 = 0.025

From z table, P(z<-1.96) = P(z>1.96) = 0.025

So critical values are -1.96 and 1.96