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Chapter 15: Chi-Square Tests
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Based on the computations so far, the chi-square statistic will be
( )
( )
( )
( )
= 50.86
Since there are 4 categories for the number of sixes rolled (0, 1, 2, and 3),
then
= 4. Thus the number of degrees of freedom for the chi-square
distribution will be
=
– 1 = 4 - 1 = 3 and the critical value is
=
7.815 (correct to three decimal places) for a level of significance equal to
0.05. This value can be obtained from the chi-square table or from the
Critical Values for the Chi-Square Distribution
workbook as shown in
Figure 15-11
.
Figure 15-11:
Chi-Square Critical Value for
Example 15-3
Thus, we can now write the hypothesis test to determine whether the die is
fair.
: The die used in the game is fair.
: The die used in the game is not fair.
:
∑
( )
= 50.86
: For a significance level 0.05, reject the null hypothesis if the
computed test statistic value,
= 50.86 >
= 7.815.
Conclusion
: Since 50.86 > 7.815, reject the null hypothesis. That
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