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.