Do college students enjoy playing sports less than watching sports? A researcher randomly selected ten college students and asked them to rate playing sports and watching sports on a scale from 1 to 10 with 1 meaning they have no interest and 10 meaning they absolutely love it. The results of the study are shown below. Playing vs. Watching Sports Data Play Watch 7 8 10 10 2 4 6 4 2 6 1 2 1 4 5 6 1 2 7 9   Assume a each population is normally distributed.  What can be concluded at  the α = 0.10 level of the significance ?(Let d = play - watch.) For this study, what sampling distribution should be used? Select an answer standard normal distribution binomial distribution uniform distribution Student t distribution  The null and alternative hypotheses would be:        H0:H0:  Select an answer μd μ1-μ2 μ p1-p2 p  Select an answer = < > ≠  (please enter a decimal)     H1:H1:  Select an answer μ p1-p2 p μd μ1-μ2  Select an answer < > = ≠  (Please enter a decimal) The test statistic? t z  = (please show your answer to 3 decimal places.)

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 + ...