Question

Use the t-distribution to find a confidence interval for a mean μ given the relevant sample results. Give the best point estimate for μ, the margin of error, and the confidence interval. Assume the results come from a random sample from a population that is approximately normally distributed.

A 95% confidence interval for μ using the sample results x̄ = 79.7, s = 6.6, and n=42

Round your answer for the point estimate to one decimal place, and your answers for the margin of error and the confidence interval to two decimal places.

Point estimate = ______

Margin of error = _______

The 95% Confidence Interval is _______

to _______

Answer 1

Given : = 79.7, s = 6.6, n = 42, = 0.05

Since population standard deviation is unknown, the tcritical (2 tail) for = 0.05, for df = n -1 = 41, is 2.02

The Confidence Interval is given by ME, where

The Lower Limit = 79.7 - 2.06 = 77.64

The Upper Limit = 79.7 + 2.06 = 81.76

The Confidence Interval is 77.64 to 81.76

The Confidence Interval is a < \mu < b