b) What is the pooled proportion of foreign born in both countries combined? c)
ID: 3369046 • Letter: B
Question
b) What is the pooled proportion of foreign born in both countries combined?
c) What is the standard error of the difference in part a?
d) What is the value of the z-statistics?
e) What do you conclude at a = 0.05
An advocacy organization surveys 1143 citizens of country A and 200 of them reported being born in another country. Similarly, 205 out of 1221 citizens of country B reported being foreign-born. The researchers want to test if the proportions of foreign born are the same in country B as in country A. Complete parts a through e below a) What is the difference in the sample proportions, p1 -P2. of foreign born residents from both countries? Assume p is the proportion of foreign born residents from country A and P2 is the proportion of foreign born residents from country B. The difference in the sample proportions, P1 P2. is Round to three decimal places as needed.)Explanation / Answer
a)
n1 = 1143
n2 = 1221
p1cap = 200/1143 = 0.175
p2cap = 205/1221 = 0.1679
p1cap - p2cap = 0.175 - 0.1679 = 0.0071
b)
pooled proportion, pcap = (200 + 205)/(1143 + 1221)
pcap = 0.1713
c)
std. error = sqrt(0.1713*(1-0.1713)*(1/1143 + 1/1221))
std. error = 0.0155
d)
Test statistics, z = (p1cap - p2cap)/SE
z = 0.0071/0.0155
z = 0.4567
e)
p-value = 0.6478
As p-value is greater than 0.05, we fail to reject the null hypothesis.
There are not sufficient evidence to conclude that the two proportions are not different.
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