Don\'t use hand writing please Thank you.... Suppose a die throw, check it is fa

Question

Don't use hand writing please

Thank you....

Suppose a die throw, check it is fair or not. If it is fair then the proportion for each value should be the same. It is need to find the observed frequencies and to accomplish this roll the die 500 times and count how often each side comes up. The data is in table. Do the data show that the die is fair? Test at the 5% level, gamma^2 cdf (5) almostequalto 0.913 Table: Observed Frequencies of Die 1. State the null and alternative hypotheses and the level of significance 2. Find the chi^2 -test. 3. Conclusion?

Explanation / Answer

1) null hypothesis:proportion of all die values are equal (=1/6)(die is fair)

alternate hypothesis:proportion of all die values are not equal.

2)

from above X2 test stat =1.5040

3)at 5% level; critical value =11.070

as chi stat is less then critical value; we can not rejct null hypothesis and conclude that the die is fair,

observed Expected Chi square X Probability O E=total*p =(O-E)^2/E 1 1/6 78.000 83.33 0.34 2 1/6 87.000 83.33 0.16 3 1/6 87.000 83.33 0.16 4 1/6 76.000 83.33 0.65 5 1/6 85.000 83.33 0.03 6 1/6 87.000 83.33 0.16 1 500 500 1.5040

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