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

Solution :

point estimate = x̄ = 79.7,

degrees of freedom = n - 1 = 42 - 1 = 41

t/2,df = 2.020

Margin of error = E = t/2,df * (s /n)

= 2.020 * ( 6.6/ 42)

Margin of error = E = 2.06

The 95% confidence interval estimate of the population mean is,

  ± E  

79.7 ± 2.06

(77.64 to 81.76)