If n=15, ¯x(x-bar)=41, and s=9, construct a confidence interval at a 90% confidence level. Assume the data came from a normally distributed population.

Question

If n=15, ¯x(x-bar)=41, and s=9, construct a confidence interval at a 90% confidence level. Assume the data came from a normally distributed population.

Give your answers to one decimal place.

_______ < μ < _______

Answer 1

Hi Salma,

This one uses the classic confidence interval in introductory statistics:

CI=x-bar +/- z*SE

Breaking this down:

x-bar=sample mean

z*=z-critical value for 90% confidence

SE=standard error

Now, identifying these variables for this problem:

x-bar=41

z*=1.645 (90% confidence is common; you might want to memorize this value)

Now, standard error has its own formula:

SE=s/sqrt(n)

s=standard deviation

n=sample size

s=9

n=15

SE=9/sqrt(15)

SE=2.324

Now, we have everything we need:

CI=x-bar +/- z*SE

x-bar=41

z*=1.645

SE=2.324

CI=41 +/- (1.645*2.324)

37.2 < mu < 44.8

I hope this helps.