Question

Conduct the hypothesis test and provide the test statistic and the critical​ value, and state the conclusion.

A person purchased a slot machine and tested it by playing it 1,133times. There are 10 different categories of​ outcomes, including no​ win, win​ jackpot, win with three​bells, and so on. When testing the claim that the observed outcomes agree with the expected​ frequencies, the author obtained a test statistic of chi squaredχ2equals=11.557. Use a 0.10 significance level to test the claim that the actual outcomes agree with the expected frequencies. Does the slot machine appear to be functioning as​ expected?

Answer 1

Solution:

Here, we have to use Chi square test for goodness of fit.

Null hypothesis: H₀: The slot machine appears to be functioning as expected.

Alternative hypothesis: H_a: The slot machine do not appears to be functioning as expected.

We are given

Number of categories = N = 10

Degrees of freedom = N – 1 = 9

Level of significance = α = 0.10

Critical Value = 14.68366

(by using Chi square table)

Test statistic = Chi square = 11.557

Test statistic value < Critical value

So, we do not reject the null hypothesis

P-value = 0.239451

(by using Chi square table)

P-value > α = 0.10

So, we do not reject the null hypothesis

There is sufficient evidence to conclude that the slot machine appears to be functioning as expected.