Question

in a random sample of 25 people, the mean commute time to work was 32.6 minutes and the standard deviation was 7.1 minutes. assume the population is normally distributed and use a t - distribution to construct a 95% confidence interval for the population mean μ. what is the margin of error of μ? interpret the results. the confidence interval for the population mean μ is (29.7, 35.5). (round to one decimal place as needed.) the margin of error of μ is. (round to one decimal place as needed.)

Explanation:

Step1: Recall the formula for margin of error

The margin of error \(E\) for a confidence interval \((\bar{x}-E,\bar{x} + E)\) is given by \(E=\bar{x}+E-\bar{x}\) (using the upper and lower bounds). Here, \(\bar{x}\) is the sample mean. The confidence interval is \((29.7,35.5)\) and the sample mean \(\bar{x}=\frac{29.7 + 35.5}{2}=32.6\) (since \(\bar{x}-E = 29.7\) and \(\bar{x}+E=35.5\)).

Step2: Calculate the margin of error

Using the formula \(E=\bar{x}+E-\bar{x}\), we substitute \(\bar{x}+E = 35.5\) and \(\bar{x}=32.6\). Then \(E=35.5 - 32.6\) (or \(E=32.6-29.7\)).

Answer:

\(2.9\)