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A casino customer is concerned about whether the dice the casino are using are "fair" (i.e.,...

A casino customer is concerned about whether the dice the casino are using are "fair" (i.e., each face is equally likely to appear). The customer obtains a die that is being used by the casino and rolls it 240 times. The customer records the following data:

Face 1 2 3 4 5 6
Frequency 46 38 44 45 38 29

What is the value of the test statistic for the goodness of fit test?

a. 19.027 b. 3.263 c. 12.956 d. 5.150

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Answer #1

The following null and alternative hypotheses need to be tested: H0 p1-0. 1667, p2-0. 1667, p3-0. 1667, p4-0.1667, p5 0.1667, p6 = 0.1667 Ha Some of the population proportions differ from the values stated in the null hypothesis This corresponds to a Chi-Square test for Goodness of Fit. (2) Rejection Region Based on the information provided, the significance level is a 0.05, the number of degrees of freedom is df 6 1 5, so then the rejection region for this test is R x2: x2> 11.07) (3) Test Statistics The Chi-Squared statistic is computed as follows x®ーΣ (0, E Ei)2 =0.897 + 0.101 +0.398 + 0.623 + 0.101+3.029 = 5.149 0.8970.1010.3980.6230.1013.029 5.149 Ei

d)5.150

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