Is your random number generator working? 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. Hint: 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 $- 0.5 t o 9.5$ 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.

Question

Accepted Answer

Part (a)

H_{0} : p 0 = p 1 = p 2 = p 3 = p 4 = p 5 = p 6 = p 7 = p 8 = p 9 = 0.1 H_{1} : A t l e a s t o n e o f t h e P_{i}' s i s i n c o r r e c t

Part (b) There is not enough proof to reject the claim of random digits.

Part (c) $0.05$

Part (d) $P (A t l e a s t o n e o f t h e 25 m a k e t y p e I e r r o r) = 0.7226$

Short Answer