Question

According to genetic theory, a particular cross of two cultivars of sorghum should produce plants with red, yellow, or white seeds in the proportions 9/16, 3/16 and 1/4. Data from an experiment yielded the following results. Red Yellow White Count 216 6785 We wish to assess whether the data agree with the theory. What is the null hypothesis for the test? There is no difference among the colours. The probabilities given by genetic theory are correct. The probabilities are not as stated. (1 pt(s)] Incorrect. Tries 1/1 Previous Tries What is the expected count for Red seeds? 207 [3 pt(s)] You are correct. Your receipt no. is 155-6962 Previous Tries Compute the value of the test statistic. 13 pt(s) Submit Answer Incorrect. Tries 1/3 Previous Tries How many degrees of freedom are there? Submit Answer Tries 0/3 [1 pt(s)]

Answer 1

1)Null Hypothesis H0: The probabilities given by genetic theory are correct.

2) Expected count for red seeds =

$E(Red) = \frac{9}{16}\times 368 = 207$

$E(White) = \frac{1}{4}\times 368 = 92$

$E(Yellow) = \frac{3}{16}\times 368 = 69$

3) Under null hypothesis , the test statistic is

$\chi ^{2} = \sum \frac{(f-e)^{2}}{e} = \frac{(214 -207)^2}{207}+\frac{(65-69)^{2}}{69}+\frac{(89-92)^{2}}{92} =0.566$

4) Degrees of Freedom = n-1 = 3-1 = 2

5) The P-Value is 0.75352

P value >0.1

Conclusion : There is no evidence against the null hypothesis that the probabilities given given by genetic theory hold.