Question

We intend to estimate the average driving time of a group of commuters. From a previous study, we believe that the average time is 42 minutes with a standard deviation of 10 minutes. We want our 90 percent confidence interval to have a margin of error of no more than plus or minus 2 minutes. What is the smallest sample size that we should consider

Answer 1

The smallest sample size that we should consider is 68.

Explanation:

We have that to find our
level, that is the subtraction of 1 by the confidence interval divided by 2. So:

Now, we have to find z in the Ztable as such z has a pvalue of
.

That is z with a pvalue of
, so Z = 1.645.

Now, find the margin of error M as such

In which
is the standard deviation of the population and n is the size of the sample.

Standard deviation of 10 minutes.

This means that

What is the smallest sample size that we should consider?

This is n for which M = 2. So

Rounding up:

The smallest sample size that we should consider is 68.