Question

You suspect that an unscrupulous employee at a casino has tampered with a die; that is, he is using a loaded die. In order to test this claim, you roll the die 200 times and obtain the following frequencies: (You may find it useful to reference the appropriate table: chi-square table or F table) Click here for the Excel Data File Category 1 2 3 4 5 6 Frequency 40 35 33 30 33 29 a. Choose the appropriate alternative hypothesis to test if the population proportions differ. All population proportions differ from 1/6. Not all population proportions are equal to 1/6.

b. Calculate the value of the test statistic. (Round intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.)

Answer 1

Solution :

a) The null and alternative hypotheses would be as follows :

H_{​​​​​​0} : All population proportions are equal to 1/6.

H_{​​​​​​1} : Not all population proportions are equal to 1/6.

b) To test the hypothesis we shall use chi-square test. The test statistic is given as follows :

Where, Oi's are observed frequencies and ei's are expected frequencies.

We are given the observed frequencies. The expected frequencies would be as follows :

Under H_{​​​​​​0} all the proportions are equal to 1/6.

Total frequency = 200

Hence, for each of the categories the expected frequency would be 200/6 = 33.3333.

From the above table we get,

The value of the test statistic is 2.320.