TEST OF GOODNESS OF FIT

# TEST OF GOODNESS OF FIT

C
10 million points

1) The offspring of a certain cross gave the following colors, red, black or white in the ratio $9$:$3$;$4$. If the experiment gave $74$, $32$ and $38$ offsprings in the categories respectively, can the theory be substantiated?

TEST OF
chegendungu

C
10 million points
- - - -
RED BLACK WHITE TOTAL
72 32 38 144
9 3 4 16

The expected frequencies are calculated as follows:

Red: $(9/16)144=54$

Black: $(3/16)144=27$

White: $(4/16)144=36$

$$\tilde{\chi}^2 = \frac{(74 – 54)^2}{54}+\frac{(32 – 27)^2}{27}+\frac{(38 – 36)^2}{36} = 8.45$$\

$$\tilde{\chi}^2 = 8.45$$\

The D.F $$n – 1$$ $$3-1$$ $$=2$$

The calculated $\tilde{\chi}^2$ of $8.45$ is greater than the table $\tilde{\chi}^2$ value of $5.99$ at $\alpha = 0.05$ and d.f $2$.

Therefore, we conclude that the number of offsprings in the $3$ colors are not compatible with the given ratios. i.e we reject the null hypothesis.

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