Suppose Jamal is studying poverty in his economics class, and he wants to compar

Question

Suppose Jamal is studying poverty in his economics class, and he wants to compare the proportion of individuals living below the poverty line in the midwestern United States in different years. He collects data on a simple random sample of people from 2013 and from the same set of people in 2014. His data arc summarized in the table. Jamal wants to run a two-sample z-test for the difference of two proportions to test the alternative hypothesis. H_1: P_1 = P_2, against the null hypothesis, H_0: P_1 = P_2, where P_1 is the proportion of population in 2013 that arc living below the poverty line, and P_2 is the proportion of population in 2014 that are living below the poverty line. Jamal selects a significance level of alpha = 0.05. Compute the z-statistic and p-value for Jamal's z-test for the difference of two proportions. P_1 - P_2. Give your answers precise to three decimal places.

Explanation / Answer

z = (p1^ -p2^)/SE(p1-p2)

SE (p1-p2) = Ö [ PQ * ((1/n1)+(1/n2))]

P = (x1+x2)/ (n1+n2)

Q = 1 – P

We are given,

p1^ = 0.13889

p2^ = 0.12963

P = (x1+x2)/ (n1+n2) = (75+70)/(540+540)= 0.13426

Q = 1 – P = 1 - 0.13426 = 0.86574

z = (0.13889-0.12963)/Ö[ (0.13426*0.86574)*((1/540)+(1/540))]

z = 0.446

P-value = P ( z > 0.446 ) = =1-NORMSDIST(0.446) [ Excel Formula ]

              = 0.328

P-value is 0.328

Answer:

z = 0.446

P-value is 0.328

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