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 are summarized in the table. Population description population in 2013 population in 2014 Sample size ni =540 2=540 Number of successes x, = 75 X2 = 70 Population Proportion of sucesses pi = 0.13889 p2 = 0.12963 2 Jamal wants to run atwo-sample z-test for the difference of two proportions to test the alternative hypothesi : p.> p2 , against the null hypothesis, Ho: Pi P2 where pi is the proportion of population in 2013 that are living below the poverty line, and P2 is the proportion of population in 2014 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-P Give vour answers precise to three decimal places scroll p-value = z-statistic =

Explanation / Answer

Given that,
sample one, x1 =75, n1 =540, p1= x1/n1=0.139
sample two, x2 =70, n2 =540, p2= x2/n2=0.13
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 =(0.139-0.13)/sqrt((0.134*0.866(1/540+1/540))
zo =0.446
| zo | =0.446
critical value
the value of |z | at los 0.05% is 1.645
we got |zo| =0.446 & | z | =1.645
make decision
hence value of |zo | < | z | and here we do not reject Ho
p-value: right tail - Ha : ( p > 0.4463 ) = 0.3277
hence value of p0.05 < 0.3277,here we do not reject Ho
ANSWERS
---------------
null, Ho: p1 = p2
alternate, H1: p1 > p2
test statistic: 0.446
critical value: 1.645
decision: do not reject Ho
p-value: 0.3277
we do not have enough evidence to support the claim that jamals Z test for difference of proportion

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