We want to test whether males are taller than females. Heights of males and females are collected and the excel outputs are given below. Assume height is normally distributed for males and females with equal variances.   t-Test: Two- sample Assuming Equal Variances    Male Female Mean 170.86 169.1333 Variance 11.2249 15.93636 Observations 50 45 Pooled Variance 13.45398   Hypothesized Mean Difference 0   df 93   t Stat 2.290934   P(T<=t) one-tail 0.012113   t Critical one-tail 1.416397   P(T<=t) two-tail 0.024226   t Critical two-tail 1.770027     t-Test: Two-Sample assuming unequal variances:    Male Female Mean 170.86 169.1333 Variance 11.2249 15.93636 Observations 50 45 Hypothesized Mean Difference  0   df 86   t Stat 2.269888   P(T<=t) one-tail 0.012857   t critical one-tail 1.417327   P(T<=t) two-tail 0.025715   t Critical two-tail 1.771619   You are given two excel outputs. Select the appropriate excel output to answer questions. Write down the  p-value for this test given in the table (give you answer to 4 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 + ...