Question

An experimenter suspects that a certain die is "loaded;" that is, the chances that the die lands on different faces are not all equal. Recall that dice are made with the sum of the numbers of spots on opposite sides equal to 7: 1 and 6 are opposite each other, 2 and 5 are opposite each other, and 3 and 4 are opposite each other.

The experimenter decides to test the null hypothesis that the die is fair against the alternative hypothesis that it is not fair, using the following test. The die will be rolled 30 times, independently. If the die lands with one spot showing 9 times or more, or 0 times, the null hypothesis will be rejected.

The power of this test against the alternative hypothesis that the chance the die lands with one spot showing is A%, the chance the die lands with six spots showing is B%, and the chances the die lands with two, three, four, or five spots showing each equal 1/6, is:

A and B is not a clear number, please include A and B in the result.

Answer 1

the significance level =P(reject | null is true )=P(X>=9)÷P(X<=0) where X is # times 1 spot shows in 30 trials,binomial with n=30 and p=1/6(null=fair die) so both the probabilities can be obtained from the tool.