An experimenter suspects that a certain die is \"loaded;\" that is, the chances

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 21.09%, the chance the die lands with six spots showing is 12.24%, and the chances the die lands with two, three, four, or five spots showing each equal 1/6, is ______?

If you are using a particular formula to solve this question, could you please let me know which formulas these are?

Explanation / Answer

The power of this test against the alternative hypothesis is the chance die lands with one spot showing is 21.09%, chance the die lands with six spot showing is 12.24%. And the chance that die lands with two, three, four, or five showing each equal 1/6 is =100% - (21.09%+12.24 %)

= 66.67%

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