Question

The probability of individuals with blood types A, B, AB and O are 0.45, 0.13,
0.06 and 0.36, respectively. A geneticist tested 100 individual blood types and
found that 40 had type A, 18 had type B, 5 had type AB and 37 had type O. Use
goodness of fit test at 5% level of significance to test whether the observed
frequencies closely correspond to the theoretical ones.

Answer 1

Answer on Question #55134 – Math – Statistics and Probability

The probability of individuals with blood types A, B, AB and O are 0.45, 0.13, 0.06 and 0.36, respectively. A geneticist tested 100 individual blood types and found that 40 had type A, 18 had type B, 5 had type AB and 37 had type O. Use goodness of fit test at 5% level of significance to test whether the observed frequencies closely correspond to the theoretical ones.

Solution

Test statistic is

$$\chi^{2} = \frac{(40 - 45)^{2}}{45} + \frac{(18 - 13)^{2}}{13} + \frac{(5 - 6)^{2}}{6} + \frac{(37 - 36)^{2}}{36} = 2.673.$$

The critical value for $4 - 1 = 3$ degrees of freedom and $5\%$ level of significance is

$$\chi_{crit}^{2} = 7.82.$$

$\chi^{2} < \chi_{crit}^{2}$, thus the observed frequencies closely correspond to the theoretical ones.

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