Question

In a flowering plant species, snapdragons, variation in flower color is determined by a single gene. RR genotype individuals are red, Rr genotype individuals are pink, and rr genotype individuals are white. In a cross between two heterozygous (Rr) individuals, the expected ratio of red:pink:white-flowered offsprings is 1:2:1. Biologists did two cross experiments, and ask whether the results differ significantly from the expected.

Part 1: The first cross experiment ends up with 40 offsprings, including 10 red, 21 pink, and 9 white.

1) Write the null and alternative hypothesis for the chi-square test.

2) Use R to conduct the chi-square and determine the p-value.

3) Interpret the p-value and state the conclusion from your test.

Part 2: The second cross experiment ends up with 4000 offsprings, including 1000 red, 2100 pink, and 900 white.  

1) Use R to conduct the chi-square and determine the p-value.

2) Now can we reject the null hypothesis? Explain

Answer 1

Part 1:

1)

Null Hypothesis H0: The ratio of red:pink:white-flowered offsprings is 1:2:1.

Alternative Hypothesis H0: The ratio of red:pink:white-flowered offsprings is not 1:2:1.

2)

x <- c(10,21,9)
p <- c(1/4,2/4,1/2)
chisq.test(x, p = p, rescale.p = TRUE)

Running the R code, we get output as below.

> chisq.test(x, p = p, rescale.p = TRUE)   

Chi-squared test for given probabilities data: x

X-squared = 5.125, df = 2, p-value = 0.07711172

P-value = 0.07711172

3)

Since, p-value is greater than 0.05 significance level, we fail to reject null hypothesis H0.

We conclude that there is no strong evidence to reject the claim that ratio of red:pink:white-flowered offsprings is 1:2:1.

Part 2:

1)

x <- c(1000,2100,900)
p <- c(1/4,2/4,1/2)
chisq.test(x, p = p, rescale.p = TRUE)

Running the R code, we get output as below.

> chisq.test(x, p = p, rescale.p = TRUE)   

Chi-squared test for given probabilities data: x

X-squared = 512.5, df = 2, p-value < 2.2204e-16

P-value = 2.2204e-16

2)

Since, p-value is less than 0.05 significance level, we reject null hypothesis H0.

We conclude that there is strong evidence from the sample data that ratio of red:pink:white-flowered offsprings is not 1:2:1.