Question

Using a T-Interval on your calculator to find a 95% confidence interval estimate of a mean when the sample mean from a sample of 35 individuals is 132.5 and the sample standard deviation is 14.7, what is the resulting margin of error?

Answer 1

The provided sample mean is 132.5 and the sample standard deviation is s = 14.7s. The size of the sample is n = 35 and the required confidence level is 95%.

The number of degrees of freedom are df = 35 - 1 = 34 , and the significance level is α=0.05.

Based on the provided information, the critical t-value for α=0.05 and df = 34 degrees of freedom is t_c = 2.032

The 95% confidence for the population mean μ is computed using the following expression

Therefore, based on the information provided, the 95 % confidence for the population mean μ is

which completes the calculation.

Margin of error = Length of confidence interval / 2

Margin of error = ( 137.55 - 127.45 )/2

Margin of error = 10.1/2

Margin of error = 5.05