Answer:
The narrowest confidence interval is obtained with a sample size of 2000 and a 95% confidence interval
Step-by-step explanation:
The confidence interval is the interval
where
= the mean of the sample
<em>s = the standard deviation of the sample
</em>
<em>n = the size of the sample
</em>
<em>z is the z-score corresponding to the level of confidence
</em>
In any case, the width of the interval is 2 times , so we only need to see which value of is the smallest between the different options.
<em>The values of z can be computed either with tables or a spreadsheet.
</em>
Sample size of 1000 and a 95% confidence interval
Sample size of 1000 and a 99% confidence interval
Sample size of 2000 and a 95% confidence interval
Sample size of 2000 and a 99% confidence interval
And we see that the narrowest confidence interval is obtained with a sample size of 2000 and a 95% confidence interval