Question

Question #3:

A study finds that

a random sample of 57 butterflies captured in a given natural

habitat is made up of 12 blue, 19 yellow, and 26 white butterflies. Is this significant evidence that

blue, yellow, and white butterflies are not equally represented in the habitat's population of

butterflies?

Test the null hypothesis of equal representation of the three butterfly colors at significance level

5%. Follow the five steps to answer this question.

Step 1:state the null hypothesis and the alternative

Step 2:significance level =

Step 3: calculate chi-square value

Step 4: calculate p-value using chi-square table

Step 5: compare p-value to significance level and take a decision.

Answer 1

Step1 :The null and alternative hypothesis

H0: There is equal representation of three butterfly colors.

Ha: There is not equal representation of three butterfly colors.

Step2:

Step 3 :

Test statistic

where

Oi : observed frequency

Ei : expected frequency

Calculation :

Color	Oi	Ei	(Oi-Ei)^2/Ei
Blue	0.33*57=19	12	4.0833
Yellow	0.33*57=19	19	0
White	0.33*57=19	26	1.8846
			5.9679

Therefore ,

Step 4 : df = 3-1=2

From chi square table with df =2

0.5 < P value <0.10

Note : From table, we can see that for df =2  

Using P value calculator , P value = 0.0506

Step 5 : P value > 0.05 (significance level)

We fail to reject H0

There is not sufficient evidence to conclude that blue , yellow and white butterflies are not equally represented in habitat's population of butterflies.