Question

in a random sample of 27 people, the mean commute time to work was 34.4 minutes and the standard deviation was 7.2 minutes. assume the population is normally distributed and use a t - distribution to construct a 98% 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 (31.0, 37.8) (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 formula for the margin of error \(E\) when using the \(t -\)distribution is \(E = t_{\alpha/2}\frac{s}{\sqrt{n}}\). Also, we can find \(E\) using the formula \(E=\frac{\text{Upper bound}-\text{Lower bound}}{2}\)

Step2: Calculate the margin of error using the confidence interval bounds

We are given the confidence interval \((31.0,37.8)\).
Substitute the values into the formula \(E=\frac{37.8 - 31.0}{2}\)

$$E=\frac{6.8}{2}$$

Answer:

\(3.4\)