A marketing executive wants to understand the differences in customer satisfaction scores between two companies offering the same service. The executive collects the following data for customer satisfaction. Assume the two populations have the same variance.  Assuming that the two populations have equal variances, what is the critical t-value for a 99% confidence interval (same as for a two-sided test at a 1% significance level) for the difference between the population means? Round your answer to three decimal places.  Assuming equal variances, what is the standard error of the difference in sample means (the standard deviation of the sample mean from company 1 minus the sample mean from company 2)? Round your answer to three decimal places.    Company 1 Company 2 1 4 7 1 10 0 3 2 7 0 8 2 3 2 6 3 7 2 1 2 7 4 9 6 9 3 4 0 10 2 8 1 9 10 8 7 5 0 10 1 2 4 3 7 2 0 9 10 8 1 3 3 5 2 8 2 9 10 7 6 4 8 4 3 1 5 0 4 5 2

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 + ...