Give your answer to two decimal places.

Question

If n=18, (x-bar)=32, and s=2, find the margin of error at a 90% confidence level

Give your answer to two decimal places.

Answer 1

Hi Kaitlyn,

This is a z-confidence interval. First, we need the standard error. This is:

SE=x-bar/sqrt(n)

Therefore, we have:

x-bar=32

s=2

n=18

SE=32/sqrt(18)

SE=0.47

Now, we need a z-critical value (z*), which you can derive from the z-table, but 90% confidence intervals are relatively common, so you might want to memorize this value: 1.645.

Now, to compute a confidence interval, the formula is:

CI=x-bar +/- (z*SE)

Here:

x-bar=32

SE=0.47 (from above)

z*=1.645

Thus,

CI=32 +/-(1.645*0.47)

CI=32+0.77

CI=(31.23, 32.77)

Margin of error is essentially the back half of the confidence interval, z*SE, so:

Margin of error=0.77

I hope this helps.