Answer: To find the margin of error and construct a 90% confidence interval for the population mean, we can use the following formula:
Margin of error = t-value x (standard deviation / square root of sample size)
where t-value is the value obtained from the t-distribution table with n-1 degrees of freedom and a confidence level of 90%.
For a sample size of 8 and a confidence level of 90%, the degrees of freedom is 7 and the t-value is 1.895 (obtained from a t-distribution table).
Using the given values, we can calculate the margin of error as:
Margin of error = 1.895 x (7.9 / sqrt(8)) ≈ 5.69 (rounded to one decimal place)
So the margin of error is approximately 5.69 miles.
To construct a 90% confidence interval for the population mean, we can use the formula:
Confidence interval = sample mean ± margin of error
Substituting the values, we get:
Confidence interval = 18.5 ± 5.69
So the 90% confidence interval for the population mean is (12.81, 24.19).
Interpretation:
We are 90% confident that the true mean driving distance to work for the population lies between 12.81 and 24.19 miles. This means that if we were to take many samples of 8 people and calculate the confidence interval for each sample, 90% of those intervals would contain the true population mean. The margin of error is the amount by which the sample mean may differ from the true population mean.
Explanation: