Use your calculator’s RandInt function to generate 200 digits from 0 to 9 and store them in a list.

a. State appropriate hypotheses for a chi-square test for goodness of fit to determine whether your calculator’s random number generator gives each digit an equal chance of being generated.

b. Carry out a test at the α = 0.05 significance level. To obtain the observed counts, make a histogram of the list containing the 200 random digits, and use the trace feature to see how many of each digit were generated. You may have to adjust your window to go from −0.5 to 9.5 with an increment of 1.

c. Assuming that a student’s calculator is working properly, what is the probability that the student will make a Type I error in part (b)?

d. Suppose that 25 students in an AP® Statistics class independently do this exercise for homework and that all of their calculators are working properly. Find the probability that at least one of them makes a Type I error.