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 different regions of the United States. He collects data on a random sample of people residing in Alabama and a random sample of people residing in Vermont. His data are summarized in the table Sample Population description residents of southern states residents of northeastern states Number of successes x, 88 X2 = 57 Proportion Population size n = 535 712 = 452 of sucesses Pi = 0.16449 Pa = 0.12611 2 Jamal wants to run a two-sample z-test for the difference of two proportions to test the alternative hypothesis H! : pl > p2, against the null hypothesis, Ho. pl = P2, where p! is the proportion of residents of southern states that are living below the poverty line, and p2 is the proportion of residents of northeastern states that are living below the poverty line. Jamal selects a significance level of = 0.05 Compute the z-statistic and p-value for Jamal's z-test for the difference of two proportions, pi -P2 precise to three decimal places nswers Scroll z-statistic = p-value

Explanation / Answer

Given that,
sample one, x1 =88, n1 =535, p1= x1/n1=0.164
sample two, x2 =57, n2 =452, p2= x2/n2=0.126
null, Ho: p1 = p2
alternate, H1: p1 > p2
level of significance, = 0.05
from standard normal table,right tailed z /2 =1.645
since our test is right-tailed
reject Ho, if zo > 1.645
we use test statistic (z) = (p1-p2)/(p^q^(1/n1+1/n2))
zo =(0.164-0.126)/sqrt((0.147*0.853(1/535+1/452))
zo =1.697
| zo | =1.697
critical value
the value of |z | at los 0.05% is 1.645
we got |zo| =1.697 & | z | =1.645
make decision
hence value of | zo | > | z | and here we reject Ho
p-value: right tail - Ha : ( p > 1.6969 ) = 0.04485
hence value of p0.05 > 0.04485,here we reject Ho
ANSWERS
---------------
null, Ho: p1 = p2
alternate, H1: p1 > p2
test statistic: 1.697
critical value: 1.645
decision: reject Ho
p-value: 0.04485
we have enough evidence to support the claim that jamals test for difference of proportions

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