Question

Pedro thinks that he has a special relationship with the number 6. In particular, Pedro thinks that he would roll a 6 with a fair 6-sided die more often than you'd expect by chance alone. Suppose pp is the true proportion of the time Pedro will roll a 6.

Required:
a. State the null and alternative hypotheses for testing Pedro's claim.
b. Now suppose Pedro makes 42 rolls, and a 6 comes up 9 times out of the 42 rolls. Determine the P-value of the test: P-value.
c. Does this sample provide evidence at the 5% level that Pedro rolls a 6 more often than you'd expect?

Answer 1

Explanation:

a) The sample space, n(S) = 6^6 = 46656

Let the number fair dice toss that show 6 = n(A)

Hence, the probability of getting, P(A) = n(A)/n(S)

b) Sample space, n(S) = 6^42

n(A) = 6^9

∴ P(A) = n(A)/n(S) = 6^9/6^42 = 1/(6^33) = 2.09 X 10^(-26)

c) No