# Testing Hypothesis

• Jan 7th 2009, 12:01 AM
zorro
Testing Hypothesis
The following table gives the observed and expected frequencies in tossing a dice 120 times. For testing the hypothesis that the dice is fair , one is required to compute $\displaystyle \chi^2$
Find the value.

$\displaystyle \begin{array}{|c|c|c|c|c|c|c|c|} Dice\ face&1&2&3&4&5&6\\ \hline Observed\ frequency&25&17&15&23&24&16\\ \end{array}$
• Jan 7th 2009, 11:19 PM
Constatine11
Quote:

Originally Posted by zorro
The following table gives the observed and expected frequencies in tossing a dice 120 times. For testing the hypothesis that the dice is fair , one is required to compute $\displaystyle \chi^2$
Find the value.

$\displaystyle \begin{array}{|c|c|c|c|c|c|c|c|} Dice\ face&1&2&3&4&5&6\\ \hline Observed\ frequency&25&17&15&23&24&16\\ \end{array}$

First compute the expected frequencies under the hypothesis

$\displaystyle \begin{array}{|c|c|c|c|c|c|c|c|} \hline Dice\ face&1&2&3&4&5&6\\ \hline Observed\ frequency&25&17&15&23&24&16\\ \hline Expected\ frequency&20&20&20&20&20&20\\ \hline \end{array}$

Now look up the $\displaystyle \chi ^2$ test equations.

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• Jan 8th 2009, 12:39 AM
zorro
hw did u get E[x]
Quote:

Originally Posted by Constatine11
First compute the expected frequencies under the hypothesis

$\displaystyle \begin{array}{|c|c|c|c|c|c|c|c|} \hline Dice\ face&1&2&3&4&5&6\\ \hline Observed\ frequency&25&17&15&23&24&16\\ \hline Expected\ frequency&20&20&20&20&20&20\\ \hline \end{array}$

Now look up the $\displaystyle \chi ^2$ test equations.

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Hw did u get Expected frequency as 20

isnt E[x] = x f(x) = 7/2
• Jan 8th 2009, 01:26 AM
Constatine11
Quote:

Originally Posted by zorro
Hw did u get Expected frequency as 20

isnt E[x] = x f(x) = 7/2

There are 120 throws and 6 equally likely outcomes, hence the expected frequency of each outcome is 120/6=20.
This is the expected number of 1, 2, .. 6's in 120 throws.

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