Question

Suppose that you interview 1000 exiting voters about who they voted for governor. Of the 1000 voters, 475 reported that they voted for the democratic candidate. Is there sufficient evidence to suggest that the democratic candidate will lose the election at the .01 level? (Hint you need 50% of the existing vote to win.

a) z = - 1.22 with a p value of .1112 .1112 > .01 Therefore there is NOT sufficient evidence to support the alternative hypothesis that the the governor will lose the election.

b) z = 1.58 with a p value of .9429 .9429 > .01 Therefore there is NOT sufficient evidence to support the alternative hypothesis that the the governor will lose the election.

c) z = - 1.58 with a p value of .0571 .0571 > .05 Therefore there is NOT sufficient evidence to support the alternative hypothesis that the the governor will lose the election.

d) z = - 1.58 with a p value of .0571 .0571 > .01 Therefore there is NOT sufficient evidence to support the alternative hypothesis that the the governor will lose the election.

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is

H₀ : p = 0.5

H_a : p 0.5

n = 1000

x = 475

= x / n = 475 / 1000 = 0.475

P₀ = 0.5

1 - P₀ = 1 - 0.5 = 0.5

z = - P₀ / [P_{0 *} (1 - P₀ ) / n]

=0.475 - 0.5 / [(0.5 * 0.5) / 1000]

= -1.58

Test statistic = -1.58

P(z <-1.58 ) = 0.0571

P-value = 2 * 0.0571 = 0.1142

= 0.05

P-value >

Fail to reject the null hypothesis .

a) z = - 1.22 with a p value of .1112 .1112 > .01 Therefore there is NOT sufficient evidence to support the alternative hypothesis that the the governor will lose the election.