Question

idk if its a left tailed or right tailed z test, or a left tailed t test, or a two tailed z test. Im also having trouble finding the p vale

Jump to level 1 A political campaign is interested in whether city 1 has more support for raising the minimum wage than city 2. Polls were conducted in the two largest cities in the state about raising the minimum wage. In city 1, a poll of 800 randomly selected voters found that 277 supported raising the minimum wage. In city 2, a poll of 1000 randomly selected voters found that 311 supported raising the minimum wage. What type of hypothesis test should be performed? Right-tailed z-test ội - Ex: 0.123 0 Ô 2 = Ex: 0.123 0 ộ Ex: 0.123 © Test statistic - Ex: 0.12 © p-value Ex: 0.123 0 Does sufficient evidence exist to support the claim that the level of support in city 1 is higher than that of city 2 at the a = 0.01 significance level? Select

Answer 1

Let $p_1,p_2$ denote the true proportions of support in city 1 and city 2 respectively.

Type of test - Right tailed Z test

Hypotheses : To test null hypothesis H. : P1 - P2 = 0 against alternative hypothesis H1 P1 - P2 > 0 Let P1, P2 denote the respective sample proportions and n1, n2 denotes the sample sizes respectively. Here, 311 P1 277 800 0.346, ni = 800, P2 0.311, n2 = 1000 1000 The test statistic can be written as: (PI -P2) – 0 2 = P1*(1-P) ni + P2*(1-P2) n2 which under Ho follows a standard normal distribution. Decision rule / Rejection region : We reject H, at 0.01 level of significance if P-value < 0.01 or if Zobs > 20.01 = 2.326348 0.4 0.3 density 0.1 - 0.0- Z Now, The value of the test statistic Zobs 1.580813 1.581 (0.346 – 0.311) 0.346*(1-0.346) 0.311*(1-0.311) + 800 1000 The critical value = 2.326348 2.33 P-value = P(Z > Zobs) = P(Z <1.580813) = (1 -0.943040) = 0.056960 – 0.0570 Conclusion : Since p-value > 0.01 and Zobs > Zcritical = 2.326348, so We fail to reject Ho at 0.01 level of significance Hence, we can conclude that the the first population proportion is not significantly greater than second population proportion.

ans-> No