Question

A researcher crossed several randomly chosen pink tree peonies, Paeonia suffruticosa, to test a genetic model of inheritance. She expected to see red:pink:white offspring colors in the ratio of 12:3:1. Below are the observed color proportions of the 83 plants in the study:

Observed Proportions of Progeny Colors

Red 0.747, Pink 0.205, White 0.048

Conduct a hypothesis test to determine if the observed proportions significantly differ from the expected ration. Given: critical = 5.99

Answer 1

Solution:

Here, we have to use chi square test for goodness of fit.

Null hypothesis: H₀: the observed proportions are not significantly differing from the expected ration.

Alternative hypothesis: H_a: the observed proportions are significantly differing from the expected ration.

We assume level of significance = α = 0.05

Test statistic formula is given as below:

Chi square = ∑[(O – E)^2/E]

Where, O is observed frequencies and E is expected frequencies.

We are given

N = 3

Degrees of freedom = df = N – 1 = 3 – 1 = 2

α = 0.05

Critical value = 5.99

(by using Chi square table or excel)

Calculation tables for test statistic are given as below:

	Obs. Prop.	Exp. Prop.	O	E	(O - E)^2/E
Red	0.747	0.75	62.001	62.25	0.000996
Pink	0.205	0.1875	17.015	15.5625	0.135566667
White	0.048	0.0625	3.984	5.1875	0.279212
Total	1	1	83	83	0.415774667

Test Statistic = Chi square = ∑[(O – E)^2/E] = 0.415774667

χ² statistic = 0.4158

P-value = 0.812298551

(By using Chi square table or excel)

P-value > α = 0.05

Or

Test statistic value 0.4158 is less than critical value 5.99.

So, we do not reject the null hypothesis

There is not sufficient evidence to conclude that the observed proportions are significantly differing from the expected ration.