Final answer:
To construct a 90% confidence interval for the population mean driving distance to work, we use the t-distribution with the given sample data. The margin or error is approximately 5.702 miles, and the confidence interval is (12.398, 23.802) miles.
Step-by-step explanation:
To construct a 90% confidence interval for the population mean driving distance to work, we can use the t-distribution since the population standard deviation is unknown. The margin of error can be calculated using the formula:
Margin of Error = t * (standard deviation / sqrt(sample size))
For a 90% confidence level, we can find the t-value with a degrees of freedom of 10 (sample size - 1). From a t-table or using software, the t-value is approximately 1.833. Plugging in the values from the sample, the margin of error is:
Margin of Error = 1.833 * (7.8 / sqrt(11)) ≈ 5.702
To construct the confidence interval, we can subtract and add the margin of error from the sample mean:
Confidence Interval = mean ± margin of error = 18.1 ± 5.702
Therefore, the 90% confidence interval for the population mean driving distance to work is approximately (12.398, 23.802). This means that we can be 90% confident that the true population mean driving distance to work falls within this range.