Testing Hypothesis

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January 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 $\chi^2$
Find the value.

$ \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} $
January 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 $\chi^2$
Find the value.

$ \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

$ \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 $\chi ^2$ test equations.

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January 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

$ \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 $\chi ^2$ test equations.

.

Hw did u get Expected frequency as 20

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