Question

Please help me answer #3.

The chi^2 value means nothing on its own-it is used to find the probability that, assuming the hypothesis is true, the observed data set could have resulted from random fluctuations. A low probability suggests that the observed data are not consistent with the hypothesis, and thus the hypothesis should be rejected. A standard cutoff point used by biologists is a probability of 0.05 (5%). If the probability corresponding to the chi^2 value is 0.05 or less, the differences between observed and expected values are considered statistically significant and the hypothesis (that the genes are unlinked) should be rejected. If the probability is above 0.05, the results are not statistically significant; the observed data are consistent with the hypothesis. To find the probability, locate your chi^2 value in the chi^2 Distribution Table in Appendix F. The "degrees of freedom" (df) of your data set is the number of categories (here, 4 phenotypes) minus 1, so df = 3. (a) Determine which values on the df = 3 line of the table your calculated chi^2 value lies between, (b) The column headings for these values show the probability range for your chi^2 number. Based on whether there are nonsignificant (p > 0.05) or significant (p lessthanorequalto 0.05) differences between the observed and expected values, are the data consistent with the hypothesis that the two genes are unlinked and assorting independently, or is there enough evidence to reject this hypothesis?

Answer 1

1. when the computed x² statistic exceeds the critical value in the x² table for a 0.05 probability level, the null hypothesis of equal distributions can be rejected in other words the observed deviations from theoretical values are significant
2. Since The calculated x² statistic 2.14 is less than x²_(0.05) of 7.815 for degrees of freedom(df) = 3, see table below. the observed deviations from expected values are not significant and hence the null hypothesis can be accepted i.e the genes are are unlinked and assorting independently.