A movie director who combines dark humor and neo-western in his films is curious about gender preferences about his movies. His team randomly sampled 12 male and 14 female movie fans and had them score one of his movies after watching it. Here are the scores: Males: 85 59 90 81 90 88 87 87 64 82 87 63 Females: 79 79 79 83 76 77 74 85 69 75 82 77 72 63 In order to investigate whether there is enough evidence to conclude that males actually like his movies more, the test statistic is Blank 1. Fill in the blank, read surrounding text. and the p-value is Blank 2. Fill in the blank, read surrounding text. . (Hint:Assume the populations are Normal and variances are equal, Use the mean of males as Mu1)

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 + ...