How would you check whether a so-called ‘fair’ die was biased? one way would be to choose a number between 1 and 6—say 3—roll the die a large number of times and see whether or not a 3 shows up roughly 1/6 of the time. think of p as the (unknown) probability that this die will show a 3 when rolled.

(a) write a down the null and (two-sided) alternative hypotheses.
(b) you intend to roll this die 400 times. verify that the two validity conditions are met in this case.
(c) of the 400 rolls, a 3 came up 51 times. compute zo and hence the p-value.
(d) write the statistical conclusion. write the contextual conclusion.
(e) compute a 95% confidence interval for p and use your interval to test the null hypothesis specified in part (a). write your statistical conclusion. is it the same as in part (d)?
(f) what is the implicit level of significance in part (e)?