Question

Melanism in Moths. Melanism is the process by which animals produce melanin to darken body tissues and produce color variation. Researchers at Oxford University suspected increased levels of pollution in London may be influencing the evolution of Lepidoptera, a species of moth native to the area that took on one of two distinct camouflage schemes: "light" and "dark." They surveyed a sample of dark and light moths on birch trees and labelled each "conspicuous" if it was visible from 30 yards away or "inconspicuous" if it was not. The table below shows the number of moths of each color that were conspicuous and inconspicuous. Use this data to investigate the researchers' theory that increased levels of pollution might provide an advantage to "dark" moths over "light" ones.

	Conspicuous	Inconspicuous	Total
Dark	7	340	347
Light	132	16	148
Total	139	356	495

Conduct a test for the stated null and alternative hypotheses. Use ?α = and round numeric answers to four decimal places.

?0H0: The variables use of color and detectability are independent.

??HA: The variables use of color and detectability are not independent.

1. Calculate the test statistic for this hypothesis test.  ? z t X^2 F  =

2. Calculate the degrees of freedom for this hypothesis test.

3. Report the p-value for this hypothesis test out to four decimal places.

p-value =

4. Based on the p-value, we have:
A. very strong evidence
B. some evidence
C. extremely strong evidence
D. little evidence
E. strong evidence
F. Reject ?0H0
that the null model is not a good fit for our observed data.

Answer 1

Result:

Melanism in Moths. Melanism is the process by which animals produce melanin to darken body tissues and produce color variation. Researchers at Oxford University suspected increased levels of pollution in London may be influencing the evolution of Lepidoptera, a species of moth native to the area that took on one of two distinct camouflage schemes: "light" and "dark." They surveyed a sample of dark and light moths on birch trees and labelled each "conspicuous" if it was visible from 30 yards away or "inconspicuous" if it was not. The table below shows the number of moths of each color that were conspicuous and inconspicuous. Use this data to investigate the researchers' theory that increased levels of pollution might provide an advantage to "dark" moths over "light" ones.

	Conspicuous	Inconspicuous	Total
Dark	7	340	347
Light	132	16	148
Total	139	356	495

Conduct a test for the stated null and alternative hypotheses. Use ?α = and round numeric answers to four decimal places.

H0: The variables use of color and detectability are independent.

HA: The variables use of color and detectability are not independent.

1. Calculate the test statistic for this hypothesis test.  ? X^2   = 390.3773

2. Calculate the degrees of freedom for this hypothesis test. DF= 1

3. Report the p-value for this hypothesis test out to four decimal places.

P value = 0.0000

4. Based on the p-value, we have:
C. extremely strong evidence
F. Reject H0
that the null model is not a good fit for our observed data.

Chi-Square Test
Observed Frequencies
	Column variable			Calculations
	Conspicuous	Inconspicuous	Total		fo-fe
Dark	7	340	347		-90.4404	90.4404
Light	132	16	148		90.4404	-90.4404
Total	139	356	495
Expected Frequencies
	Column variable
0	Conspicuous	Inconspicuous	Total		(fo-fe)^2/fe
Dark	97.4404	249.5596	347		83.9433	32.7756
Light	41.5596	106.4404	148		196.8130	76.8455
Total	139	356	495
Data
Level of Significance	0.05
Number of Rows	2
Number of Columns	2
Degrees of Freedom	1
Results
Critical Value	3.8415
Chi-Square Test Statistic	390.3773
p-Value	0.0000
Reject the null hypothesis