A Hollywood film producer is working on a new action film. She wants to estimate the true mean length of action films that have appeared in theatres during the past decade. She randomly selects 30 films and records their run time. The 95% confidence interval for the true mean length of action films during the past decade is between about 111 minutes and 127 minutes. Is it plausible that the mean length of films during the past decade is less than 130 minutes? Yes, because 130 minutes does not lie in the interval, it is reasonable to believe that the mean length of films during the past decade is less than 130 minutes. Yes, because the entire interval of movie lengths is below her length of 130 minutes, it is reasonable to believe the mean length of films during the past decade is less than 130 minutes. No, since 130 minutes is close to the interval, it is reasonable to believe the mean length of films during the past decade is not less than 130 minutes. No, because 130 is above the interval, it is not reasonable to believe the mean length of films during the past decade is less than 130 minutes.

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 + ...