A high school biology class conducted genetics experiments with randomly selected fruit flies, and the results in the following table are based on the results that they obtained. Use a 0.05 significance level to test the claim that the observed frequencies agree with the proportions that were expected according to principles of genetics. Characteristic Frequency Expected Proportion Red Eye/ Normal Wing 71 9/16 Sepia Eye/ Normal Wing 20 3/16 Red Eye/ Vestigial Wing 12 3/16 Sepia Eye/ Vestigial Wing 9 1/16 Determine the null and alternative hypotheses.
H_(0)
: The frequency counts agree with the proportions from genetics.
H_(1)
: The frequency counts do not agree with the proportions from genetics. Calculate the test statistic,
\chi ^(2)
.
\chi ^(2)=
?
(Round to three decimal places as needed.)