Question

3. When two white-eyed insects mate, we expect due to our understanding of genetics that 25% of their children will have black eyes, 50% of their children will have white eyes, and 25% of their children will have red eyes.

a. When Tom mated two white-eyed insects in his freshman genetics course he counted 8 insect children with black eyes, 22 insect children with white eyes, and 10 insect children with red eyes. Test the null hypothesis (at the significance level α = 0.05) that his data agree with the genetics model. Calculate (or bound) the p-value. Clearly state your conclusion.

b. Tom is one of 800 students in his freshman genetics course who each independently did the same experiment. Only 38 of these students rejected the null hypothesis (at the significance level α = 0.05) that their data agreed with the genetics model. Assuming that the genetics model is correct, does this observation imply that these 38 students made mistakes? About how many students would we expect to reject the null model? Explain your answers to both questions.

Answer 1

(a)

Hypotheses are:

H0:His data agrees with the genetics model.

Ha: His data does not agree with the genetics model.

Following table shows the calculations:

	O	p	E=p*40	(O-E)^2/E
	8	0.25	10	0.4
	22	0.5	20	0.2
	10	0.25	10	0
Total	40	1	40	0.6

The test statistics is

The degree of freedom:

df=3-1=2

The p-value is 0.7408

Excel function used for p-value: "=CHIDIST(0.6,2)"

Since p-value is greater than 0.05 so we fail to reject the null hypothesis.

There is evidence to conclude that his data agree with the genetics model.

(b)

Alpha is 0.05. It shows that 5% test reject the true null hypothesis.

That is expected number of students to reject the null model si 800 *0.05 = 40.

Yes it seems that 38 students either made a mistake or their samples shows the evidence to reject the nul hypothesis.