Business statistics

Question

If n=27, x¯(x-bar)=34, and s=14, construct a confidence interval at a 99% confidence level. Assume the data came from a normally distributed population.

Give your answers to one decimal place.

 _______< μ < ________

Answer 1

When we construct a confidence interval from a sample, we want to calculate the standard error instead of just using the sample standard deviation (sometimes called the "biased" estimate of the standard deviation):

stderr(x) = s / sqrt(n) = 14 / sqrt(27) = 2.694.

A 99% confidence interval is associated with a 2.576 z-value (using a z-score table or calculator). As a result, our interval is:

x̄ - z*s/sqrt(n) < μ < x̄ + z*s/sqrt(n)

34 - 2.576 * 14/sqrt(27) * < μ < 34 + 2.576 * 14/sqrt(27)

27.0 < μ < 40.9