A study from 2014 found that adults in the US spend an average of 11 hours per day watching, reading, listening to or simply interacting with media. Researchers at UCLA suspect students spend less time engaging media. They grouped UCLA students by class section, randomly selected 20 class sections, and administered a survey to each student in those randomly selected class sections. The following data represents the mean time (in hours) per day spent engaging media for each of the randomly selected classes: 9.5 11.5 6.0 7.5 8 9.5 10.5 11 12 8.2 5 9.5 8.2 9.3 10.8 11 13 8.6 9.5 10.5 Does the sample appear to come from a population that is approximately normally distributed. Explain in detail by addressing each of the 3 Criteria for samples under size 30.

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 + ...