In: Statistics and Probability

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 1,156 times. 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 squared equals18.233. Use a 0.05 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?

**Solution:**

Given: A person purchased a slot machine and tested it by playing it 1,156 times. There are 10 different categories of outcomes, including no win, win jackpot, win with three bells, and so on.

Thus k = Number of categories = 10

The obtained test statistic of chi squared = 18.233

Level of significance = 0.05

We have to test the claim that the actual outcomes agree with the expected frequencies.

**Hypothesis of study are:**

H0: The actual outcomes agree with the expected frequencies

Vs

H1: The actual outcomes do not agree with the expected frequencies

**Test statistic:**

**Critical value:**

df = k - 1 = 10 - 1 = 9

Level of significance = 0.05

From Chi-square critical value table, we get:

Chi-square critical value = 16.919

**Decision Rule:** Reject H0, if Chi-square test
statistic value > Chi-square critical value = 16.919, otherwise
we fail to reject H0.

Since Chi-square test statistic value = 18.233 > Chi-square critical value = 16.919, we reject H0.

**Conclusion:**

Since we have rejected null hypothesis H0, there is not sufficient evidence to support the claim that the actual outcomes agree with the expected frequencies.

**Thus the slot machine does not appear to be functioning
as expected.**

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