Question

in a random sample of 20 people, the mean commute time to work was 30.7 minutes and the standard deviation was 7.1 minutes. assume the population is normally distributed and use a t - distribution to construct a 90% 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 (28.0, 33.5). (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 is given by \(E=\frac{\text{Upper bound}-\text{Lower bound}}{2}\)

Step2: Substitute the values

Given the lower bound \(L = 28.0\) and the upper bound \(U=33.5\)

$$
LATEXBLOCK0
$$

Step3: Round the result

Rounding \(2.75\) to one decimal place, we get \(2.8\)

Answer:

The margin of error of \(\mu\) is \(2.8\)