A Pew Research study conducted in 2017 found that approximately 75% of Americans believe that robots and computers might one day do many of the jobs currently done by people (Pew Research website, http://www.pewinternet.org/2017/10/04/americans-attitudes-toward-a- future-in-which-robots-and-computers-can-do-many-human-jobs/). Suppose we have the following data collected from nurses, tax auditors, and fast-food workers in which a higher score means the person feels his or her job is more likely to be automated. F = Nurse 4 5 6 3 4 5 6 4 3 4 a. Use a = 0.05 to test for differences in the belief that a person's job is likely to be automated for the three professions. (to 2 decimals) The p-value is greater than 0.10 What is your conclusion? We cannot reject the three professions. Tax Auditor 6 7 6 4 8 6 LSD = What is your conclusion? We cannot reject Fast-Food Worker 6 8 4 6 7 5 (to 2 decimals) 5 6 the null hypothesis that the mean scores are the same for b. Use Fisher's LSD procedure to compare the belief that a person's job will be automated for nurses and tax auditors. the null hypothesis that the two population means are equal.

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 + ...