Question

A political interest group wants to determine what fraction p ∈ (0, 1) of the population intends to vote for candidate A in the next election. 1000 randomly chosen individuals are polled. 457 of these indicate that they intend to vote for candidate A. Find the 95% confidence interval for the true fraction p.

Answer 1

Answer:

95% confidence interval for the true fraction p is (0.426, 0.488)

Step-by-step explanation:

Confidence Interval can be calculated using p±ME where

• p is the sample proportion ($\frac{457}{1000} =0.457$

• ME is the margin of error from the mean

and margin of error (ME) around the mean can be found using the formula

ME=$\frac{z*\sqrt{p*(1-p)}}{\sqrt{N} }$ where

• z is the corresponding statistic in 95% confidence level (1.96)
• p is the sample proportion (0.457)

• N is the sample size (1000)

then ME=$\frac{1.96*\sqrt{0.457*0.543}}{\sqrt{1000} }$ ≈ 0.031

Then 95% confidence interval would be 0.457±0.031 or (0.426, 0.488)