Question

A poll asked adults in a certain country whether immigration was a good thing or a bad thing for the country. Out of 1062 ​respondents, 384 said it was a good thing. a. What percentage of those taking the poll said immigration was a good​ thing? b. Check the conditions to determine whether you can apply the CLT to find a confidence interval. c. Find a​ 95% confidence interval for the proportion who believe immigration is a good thing.

Answer 1

Solution :

n = 1062

x = 384

= x / n = 384 / 1062 =0.362

1 - = 1 - 0.362= 0.638

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.960

Margin of error = E = Z / 2 * (( * (1 - )) / n)

=1.960 * ((0.362 * 0.638 / 1062 )

= 0.029

A 95 % confidence interval for population proportion p is ,

- E < P < + E

0.362 - 0.029 < p < 0.362 + 0.029

0.333 < p < 0.391