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 1,294 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 χ2=16.414 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?

The test statistic is:

The critical value is :

State the conclusion:

(Do not reject or Reject) H0. (There is or is not) sufficient evidence to warrant rejection of the claim that the observed outcomes agree with the expected frequencies. The slot machine (does not appear or appears) to be functioning as expected.

Answer #1

a) As we are testing here whether the actual outcomes agree with
the expected frequencies, therefore this is a chi square test for
goodness of fit here. **Therefore 16.414 is the chi square
test statistic value here.**

b) For 0.1 level of significance and k - 1 = 9 degrees of freedom, we have here from the chi square distribution tables:

**Therefore 14.6837 is the required critical chi square
distribution value.**

c) As the test statistic value here is 16.414 > 14.6837,
therefore it lies in the rejection region here and **we can
reject H0 here.**

Therefore we have sufficient evidence here that the observed outcomes do not agree with the expected frequencies. The slot machine is not functioning as expected here.

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