A researcher has a set of numbers whose mean is equal to 13.8. The researcher wants to know if that set of numbers likely comes from the uniform distribution on the

interval of 1 to 16. a. Determine the theoretical expected value for the uniform distribution on the interval of 1 to 16 using the equation method. b. With reference to the lecture slides, create the distribution of means from 99 random simulated draws from the uniform distribution on the interval from 1 to 16. C. Plot the histogram (function hist()) of the simulated distribution of means and place a vertical line on that plot at the location of the researcher's mean (abline(v=13.8)) and another line showing the theoretically expected value. d. Determine the probability that the researcher's mean comes from that distribution (the monte-carlo p-value). e. Explain your conclusion.