Question

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

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 comma 1781,178 times. There are 1010 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=12.007 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?

The test statistic is

Solution:

From the given information for the Chi-square test for goodness-of-fit, it is observed there are total 10 categories and level of significance is given as 0.05.

The test statistic is 12.007

N = number of categories = 10

Degrees of freedom = df = N - 1 = 10 - 1 = 9

Level of significance = α = 0.05

So, critical value by using Chi-square table or excel is given as below:

Critical value = 16.91898

The test statistic value is less than the critical value, so we do not reject the null hypothesis that the actual outcomes agree with the expected frequencies.

There is sufficient evidence to conclude that the actual outcomes agree with the expected frequencies.

The slot machine is appearing to be functioning as expected.