Chi square problem

**wolfyparadise** · January 1st 2010, 09:18 PM

Question : 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 its value

$\begin{array}[/font]{|c|c|c|c|c|c|c|}Dice \ face & 1 & 2 & 3 & 4 & 5 & 6 \\<br /> Observed \ freq & 25 & 17 & 15 & 23 & 24 & 16 \end{array}$
--------------------------------My Work-----------------------------------------

$\chi^2 = \frac{(f_0 - f_e)^2}{f_e}$

The dice are tossed 120 times

Pr(Of on face of die) = $\frac{1}{6}$

Freq of a die face = $\frac{\frac{1}{6}}{120} = 20$

$\therefore<br /> \chi^2 = \frac{(25-20)^2}{20} + \frac{(17-20)^2}{20} + \frac{(15-20)^2}{20} + \frac{(23-20)^2}{20} + \frac{(24-20)^2}{20} + \frac{(16-20)^2}{20}$ .....................Am i doing it correctly or no please let me know

regards
wolfy

**matheagle** · January 1st 2010, 11:31 PM

this seems right, it should be a chi-square with 5 dfs.
http://en.wikipedia.org/wiki/Goodness_of_fit

**wolfyparadise** · January 2nd 2010, 04:32 AM

thanks man
muchas gracias

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