Question

in a random sample of eleven people, the mean driving distance to work was 19.3 miles and the standard deviation was 5.5 miles. assume the population is normally distributed and use the t - distribution to find the margin of error and construct a 95% confidence interval for the population mean μ. interpret the results.
identify the margin of error.
3.7 miles
(round to one decimal place as needed.)
construct a 95% confidence interval for the population mean.
(, )
(round to one decimal place as needed.)

Explanation:

Step1: Recall the formula for confidence interval

The formula for a confidence interval using the t - distribution is \(\bar{x}\pm E\), where \(\bar{x}\) is the sample mean and \(E\) is the margin of error. We are given \(\bar{x} = 19.3\) and \(E=3.7\).

Step2: Calculate the lower and upper bounds

For the lower bound: \(19.3 - 3.7\)

$$19.3-3.7=15.6$$

For the upper bound: \(19.3 + 3.7\)

$$19.3 + 3.7=23.0$$

Answer:

\((15.6,23.0)\)