Automobile Insurance Premiums. The average annual premium for automobile insurance in the United States is $1503. The following annual premiums ($) are representative of the website’s findings for the state of Michigan. 1905 3112 2312 2725 2545 2981 2677 2525 2627 2600 2370 2857 2962 2545 2675 2184 2529 2115 2332 2442 Assume the population is approximately normal. a. Provide a point estimate of the mean annual automobile insurance premium in Michigan. b. Develop a 95% confidence interval for the mean annual automobile insurance premium in Michigan. c. Does the 95% confidence interval for the annual automobile insurance premium in Michigan include the national average for the United States? What is your inter- pretation of the relationship between auto insurance premiums in Michigan and the national average?

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 + ...