Question

Quebec vs Texas Secession In an analysis of a poll of 800 Quebecers, 28% thought that the province of Quebec should separate from Canada. Another poll of 500 Texans found that 18% thought that the state of Texas should separate from the United States.1 1" in Texas, 31% Say State Has Right to Secede From US.. But 75% Opt To Stay" Rasmussen Reports, April 17, 2009. (a) In the sample of 800 people, about how many Quebecers thought Quebec should separate from Canada? In the sample of 500, how many Texans thought Texas should separate from the US? Round your answers to the nearest integer. Quebec: Texas: (b) In these two samples, what is the pooled proportion of Texans and Quebecers that want to separate? Round your answer to three decimal places. (c) Can we conclude that the two population proportions differ? Use a two-tailed test and interpret the result. State the null and alternative hypotheses. Your answer should be an expression composed of symbols: ,μ, μ i , μ2: p, pi ,P2 ,p, p, Pi , p2 .r Use subscripts 1 for Quebec and 2 for Texas. (d) Give the test statistic and the p-value. Round your answer for the test statistic to two decimal places and your answer for the p-value to three decimal places. test statistic p-value- (e) What is the conclusion of the test? Reject Ho Do not reject Ho

Answer 1

a)

Quebec: 800*0.28 = 224

Texas: 500*0.18 = 90

b)

p = (224+90)/(800+500) = 0.242

c)

The following null and alternative hypotheses need to be tested: This corresponds to a two-tailed test, for which a z-test for two population proportions needs to be conducted 2) Rejection Region Based on the information provided, the significance level is a0.05, and the critical value for a two tailed test is1.96. The rejection region for this two-tailed test is R = {: 3) Test Statistics The z-statistic is computed as follows: > 1.96} 0.28 0.18 4.098 VP1 P)(1/ 1/n2) 0.2415 1-0.2415 1/8001/500) Since it is observed th4.0981.96, it is then concluded that the null hypothesis is rejected Using the P-value approach: The p-value is p = 0, and since p = 0 < 0.05, it is concluded that the null hypothesis is rejected. (5) Conclusion It is concluded that the null hypothesis Ho is rejected Therefore, there is enough evidence to claim that population proportion pi is different than p2, at the 0.05 significance level