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.