Chapter 26, Problem 9E

a)

To determine

To explain whether the results are consistent with theoretical distribution predicted by the genetic model.

Answer to Problem 9E

There is not sufficient evidence to reject the claim that the observed results are consistent with the theoretical distribution predicted by the genetic model.

Explanation of Solution

Given:

Fruit flies Offspring of certain fruit flies may haveyellow or ebony bodies and normal wings or short wings.Genetic theory predicts that these traits will appear in theratio 9:3:3:1 (9 yellow, normal: 3 yellow, short: 3 ebony,normal: 1 ebony, short). A researcher checks 100 such

flies and finds the distribution of the traits to be 59, 20,11, and 10, respectively.

The null and alternative hypotheses:

  $\begin{array}{l}{H}_0:p_1=\frac{9}{16},p_2=p_3=\frac{3}{16},p_4=\frac{1}{16}\\ H_a:H_a:Atleastoneofthe{p}_i’sdifferent\end{array}$

Using excel,

Observed	expected	O - E	(O - E)² / E	% of chisq
59	56.250	2.750	0.134	2.37
20	18.750	1.250	0.083	1.47
11	18.750	-7.750	3.203	56.49
10	6.250	3.750	2.250	39.67
Total = 100	100.000	0.000	5.671	100.00
5.67	chi-square
3	df
.1288	p-value

  ${\chi }^2$ = 5.67 and P-value = 0.1288

Decision: The p-value>0.05, fail to reject H0.

Conclusion: There is not sufficient evidence to reject the claim that the observed results are consistent with the theoretical distribution predicted by the genetic model.

b)

To determine

To explain whether the results are consistent with theoretical distribution predicted by the genetic model if double flies are counted.

Answer to Problem 9E

There is sufficient evidence to reject the claim that the observed results are consistent with the theoretical distribution predicted by the genetic model.

Explanation of Solution

Given:

Fruit flies Offspring of certain fruit flies may have yellow or ebony bodies and normal wings or short wings. Genetic theory predicts that these traits will appear in the ratio 9:3:3:1 (9 yellow, normal: 3 yellow, short: 3 ebony, normal: 1 ebony, short). A researcher checks 100 such

flies and finds the distribution of the traits to be 59, 20, 11, and 10, respectively.

The null and alternative hypotheses:

  $\begin{array}{l}{H}_0:p_1=\frac{9}{16},p_2=p_3=\frac{3}{16},p_4=\frac{1}{16}\\ H_a:H_a:Atleastoneofthe{p}_i’sdifferent\end{array}$

Using excel,

observed	expected	O - E	(O - E)² / E	% of chisq
118	112.500	5.500	0.269	2.37
40	37.500	2.500	0.167	1.47
22	37.500	-15.500	6.407	56.49
20	12.500	7.500	4.500	39.67
200	200.000	0.000	11.342	100.00
11.34	chi-square
3	Df
.0100	p-value

  ${\chi }^2$ = 11.34 and P-value = 0.0100

Decision: The p-value < 0.05, reject H0.

Conclusion: There issufficient evidence to reject the claim that the observed results are consistent with the theoretical distribution predicted by the genetic model.

c)

To determine

To explain the discrepancy in two conclusions.

Answer to Problem 9E

Due to different sample size.

Explanation of Solution

Given:

Fruit flies Offspring of certain fruit flies may have yellow or ebony bodies and normal wings or short wings. Genetic theory predicts that these traits will appear in the ratio 9:3:3:1 (9 yellow, normal: 3 yellow, short: 3 ebony, normal: 1 ebony, short). A researcher checks 100 such

flies and finds the distribution of the traits to be 59, 20, 11, and 10, respectively.

The sample size is different for both conclusions. We know, if the sample size is larger than the observed difference between expected and observed is also larger.