Question

Sample size: A researcher is trying to decide how many people to survey. Which of the following sample sizes will result in a confidence interval with the largest width? 300 700 1000 The width depends on the sample proportion.

Answer 1

Answer:

Step-by-step explanation:

Given that a researcher is trying to decide how many people to survey.

We have confidence intervals are intervals with middle value as the mean and on either side margin of error.

Confidence interval = Mean ± Margin of error

Thus confidence interval width depends on margin of error.

Margin of error = $Critical value *\frac{\sigma}{\sqrt{n} }$

Thus for the same confidence level and std deviation we find margin of error is inversely proportional to square root of sample size.

Hence for small n we get wide intervals.

So if sample size = 300, the researcher will get wider confidence interval