In a random sample of 23 ​people, the mean commute time to work was 31.8 minutes and the standard deviation was 7.2 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 (___,___). ​(Round to one decimal place as​ needed.)   The margin of error of μ is nothing ​(Round to one decimal place as​needed.) Interpret the results.   A.If a large sample of people are taken approximately 90​% of them will have commute times between the bounds of the confidence interval. B.With 90​% ​confidence, it can be said that the commute time is between the bounds of the confidence interval. C.It can be said that 90​% of people have a commute time between the bounds of the confidence interval. D.With 90​% ​confidence, it can be said that the population mean commute time is between the bounds of the confidence interval.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...