Question

27. given that in an initial random survey 87 of 1500 respondents stated they would not vote for candidate A and in later random survey 112 of 1600 respondents stated they would not vote for candidate A, answer the following

27.1 state/explain in your own words what the test results show

27.2 determine whether to reject or not reject the null hypothesis of no difference in the population proportions at each of alpha = 0.01, 0.05, 0.10, 0.15

Answer 1

(27.1) In the initial survey, proportion of voters against candita A is p1 = 87/1500 = 0.058. In the subsequent survey, the proportion has increased to p2 = 112/600 = 0.07.

(27.2)

Q = 1 - P= 0.9358

Test statistic is:
Z = (p1 - p2)/SE

= (0.058 - 0.07)/0.0087 = - 1.3793

(a)

= 0.01

From Table, critical values of Z = 2.576

Since calculated value of Z = - 1.3793 is greater than critical value of Z = - 2.576, Fail to reject the null hypothesis.

(b)

= 0.05

From Table, critical values of Z = 1.96

Since calculated value of Z = - 1.3793 is greater than critical value of Z = - 1.96, Fail to reject the null hypothesis.

(c) = 0.10

From Table, critical values of Z = 1.645

Since calculated value of Z = - 1.3793 is greater than critical value of Z = - 1.645, Fail to reject the null hypothesis.

(d)

= 0.15

From Table, critical values of Z = 1.44

Since calculated value of Z = - 1.3793 is greater than critical value of Z = - 1.44, Fail to reject the null hypothesis.