in 360 tosses of a pair of dice, 74 sevens and 24 elevens are observed.using a 0.05 level of significance test the hypothesis that the dice are fair.

Question

in 360 tosses of a pair of dice, 74 sevens and 24 elevens are observed.using a 0.05 level of significance test the hypothesis that the dice are fair.

Answer 1

For fair dice, P(7) = 1/6, P(11) = 1/18, and P(other) = 7/9

Then, with 360 rolls, the expected number of 7s, 11s, and others is 60, 20, and 280.

Thus, the Chi-square statistic is (74-60)^2/60 + (24-20)/^2/20 + (262-280)^2/280 =

196/60 + 16/20 + 324/280 = OR 5 47/210.

The critical statistic for chi-square p = .05 with 2 degrees of freedom is, from Excel, =CHISQ.INV.RT(0.05,2) = 5.99

5.22 < 5.99, so we fail to reject the null hypothesis that the dice are fair.

Note that we need to construct this test before the rolls, not after; otherwise, the test is not appropriate.