Question

1. Suppose a survey is conducted using a random sample to determine whether voters in a city are in favour of some project. A sample with n =100 observations is obtained, and the proportion found to be in favour of the motion is 40%

i) Construct a 95% confidence interval for the proportion among the entire population that supports the project.

ii) Construct a 99% confidence interval for the proportion among the entire population that supports the project.

iii) What influence did the increase in the confidence level have on the interval you estimated? What change to the research design would produce the same effect in repeated sampling?

Answer 1

1i.) Sample proportion = 0.4
Sample size (n) = 100
Confidence interval(in %) = 95
z @ 95% = 1.96
Since we know that

Required confidence interval = (0.4-0.096, 0.4+0.096)
Required confidence interval = (0.304, 0.496)


ii) Confidence interval(in %) = 99
z @ 99% = 2.576
Since we know that

Required confidence interval = (0.4-0.1262, 0.4+0.1262)
Required confidence interval = (0.2738, 0.5262)

iii) As confidence increased from 95% to 99%, the interval also increases. If we decrease the sample size, confidence interval will increase.


Please hit thumps up if the answer helped you.