Question

The article “Linkage Studies of the Tomato (Trans. Royal Canad. Inst. (1931): 1-19) reported the following data on phenotypes resulting from crossing tall cut-leaf tomatoes with dwarf potato-leaf tomatoes. There are four possible phenotypes: (1) tall cut-leaf, (2) tall potato-leaf, (3) dwarf cut-leaf, (4) dwarf potato-leaf. Mendel’s laws of inheritance imply that π1= 9/16, π2= 3/16, π3= 3/16, π4= 1/16. (π means probability) Using the 0.01 significance level, test to determine if the reported data are different from what we would have expected with Mendel’s laws?
  

Find: Research question

b.) Hypothesis in Words (Ho, Ha)

c.Decision rule

d.Test and Results, name of test, results

a) Research question

Answer 1

Here, probabilities of four types of phenotypes are given. So, we have observe sample data and collect observed frequencies of different types. Also using the probabilities given we have to compute expected frequencies of all four types. We have to proceed as follows.

Suppose, we observed types for N trees. Then we get as follows.

Type	Observed frequency	Expected frequency
1. Tall cut-leaf
2. Tall potato-leaf
3. Dwarf cut-leaf
4. Dwarf potato-leaf
Total	N	N

Now, we have to perform Chi-square test of goodness of fit.

We have to test for null hypothesis

against the alternative hypothesis

Number of groups

Our test statistic is given by

Based on observed and expected frequencies we obtain calculated value of test statistic as .

Level of significance

Degrees of freedom

So, critical value is given by

[Using R-code 'qchisq(1-0.01,3)']

Decision rule- We reject null hypothesis if or can not reject otherwise.