Question

The theory predicts that the population of beans in the four groups A,B, C and D

should be 9:3:3:1. In an experiment among 1600 beans,the number in the four

groups was 882,313,287 and 118. Do theexperimental results support the survey

Answer 1

$\chi^2$ test

$H_0:$ the experiment results support the theory

$H_a:$ the experiment results do not support the theory

$\chi^2=\sum \frac{(O_i-E_i)^2}{E_i}=4.72$

Degrees of freedom:

$df=4-1=3$

From table:

$\chi^2_{0.05}=7.815$

Since the calculated value of $\chi^2$  is less than the table value, the null hypothesis may be accepted

with the significance level $\alpha=5\ \%$