Testing a genetic model Biologists wish to cross pairs of tobacco plants having genetic makeup $Gg$, indicating that each plant has one dominant gene ($G$) and one recessive gene ($g$) for color. Each offspring plant will receive one gene for color from each parent. The Punnett square shows the possible combinations of genes received by the offspring.

The Punnett square suggests that the expected ratio of green ($GG$) to yellow-green ($Gg$) to albino ($gg$) tobacco plants should be $1:2:1$. In other words, the biologists predict that $25\%$of the offspring will be green, $50\%$will be yellow-green, and $25\%$will be albino. To test their hypothesis about the distribution of offspring, the biologists mate $84$randomly selected pairs of yellow-green parent plants. Of $84$offspring, $23$plants were green, $50$were yellow-green, and $11$ were albino. Do the data provide convincing evidence at the $\alpha =0.01$ level that the true distribution of offspring is different from what the biologists predict?

Step by step solution

01

Given information

We need to find out whether the data provided is convincing evidence or not.

02

Explanation

We know that

The null hypothesis asserts that the variables are unrelated, whereas the alternative hypothesis asserts that they are.

$H_0:p_1=25\%=0.25,p_2=50\%=0.50,p_3=25\%=0.25$

$H_{\alpha }:$Atleast one $p_i$ is different.

And expected frequencies are a product of row and column total divided by table total.

And The squared differences between the actual and predicted frequencies, divided by the expected frequency, make up the chi-square subtotals.

Therefore, the data is not convincing evidence that true distribution is different from prediction of biologist.

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