A company is researching the effectiveness of a new website design to decrease the time to access a website. Five website users were randomly selected, and their times (in seconds) to access the website with the old and new designs were recorded. To compare the times, they computed new website design time − old website design time. The results are shown here. User Old Website Design New Website Design A 30 25 B 45 30 C 25 20 D 32 30 E 28 27   a) What is the value of the test statistic? A) 2.256 B) 1.895 C) 3.747 D) 2.447 b) For a 0.01 significance level, what is the critical value? A) −2.256 B) −1.895 C) −3.747 D) −2.447 c) For a 0.01 significance level, what is the decision regarding the hypothesis that the training was effective in improving customer relationships? A) Reject the null hypothesis and conclude that the new design reduced the mean access times. B) Reject the null hypothesis and conclude that the new design did not reduce the mean access times. C) Fail to reject the null hypothesis. D) Fail to reject the null hypothesis and conclude that the mean access times are inaccurate.

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 + ...