Question

A certain smart phone game app allows the player, once a day, to spin a wheel with 8 different sections. Seven of the sections contain a small prize and one of the sections is the grand prize, in which the player wins all of the other seven prizes. The makers of the game claim that the wheel has an equally likely probability of landing on each section. Andraya has played the game for several months and believes that the grand prize occurs less often than the game makers claim.

Required:
What would be appropriate hypotheses for the Andraya to test?

Answer 1

The appropriate hypothesis set for Andraya to test is:

`H_0: p = 0.125`

`H_1: p < 0.125`

Explanation:

The makers of the game claim that the wheel has an equally likely probability of landing on each section.

That is, the makers claim that the probability of earning the grand prize is:

`p = (1)/(8) = 0.125`

Andraya has played the game for several months and believes that the grand prize occurs less often than the game makers claim.

At the null hypothesis, we test if it happens as often as the makers claim, that is, the proportion is 0.125. So

`H_0: p = 0.125`

At the alternate hypothesis, we test if it happens less ofter than the makers claim, that is, the proportion is less than 0.125. So

`H_1: p < 0.125`

The appropriate hypothesis set for Andraya to test is:

`H_0: p = 0.125`

`H_1: p < 0.125`