student was asked to find a 98% confidence interval for widget width using data from a random sample of size n = 15. Which of the following is a correct interpretation of the interval 11.5 < μ < 28.9? Check all that are correct. With 98% confidence, the mean width of all widgets is between 11.5 and 28.9. With 98% confidence, the mean width of a randomly selected widget will be between 11.5 and 28.9. 98% of all the widgets have a width between 11.5 and 28.9. There is a 98% chance that the mean of a sample of 15 widgets will be between 11.5 and 28.9.

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 + ...