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6 suppose a die is tossed 1000 times, and the following frequencies are obtained for the number of pips up when the die comes to a rest. x1 x2 x3 x4 x5 x6 163 178 142 150 183 184 using the chi-squared goodness of fit test, assess whether we have evidence that this is not a symmetrical die. record the standardized residuals

Answer :

We have evidence that this is not a symmetrical die the standardized residuals is 9.5699.

Given that,

The following frequencies are found for the number of pips up when the die comes to rest, assuming a die is tossed 1000 times. Find out if there is proof that this die is not symmetrical using the chi-squared goodness of fit test. The standardized residuals should be noted.

x₁           x₂           x₃           x₄         x₅           x₆

163        178        142        150       183        184

We know that,

          observed       expected         Op-Ep         (Op-Ep)²/Ep

x₁          163                 166.7                -3.7               0.082

x₂          178                 166.7                 11.3              0.7659

x₃          142                 166.7                -24.7            3.6598

x₄          150                 166.7                -16.7             1.673

x₅          183                 166.7                16.3               1.5938

x₆           184                 166.7               17.3               1.7954

                                                                                 -----------

                                                                                 9.5699

Expected = 1/nΣXa=1/6(1000)=166.7

Therefore, We have evidence that this is not a symmetrical die the standardized residuals is 9.5699.

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