Question

A particular article reported the accompanying 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, and (4) dwarf potato-leaf.

	Phenotype
	1	2	3	4
Frequency	926	288	295	101

Mendel's laws of inheritance imply that p₁ = 9/16, p₂ = 3/16 , p₃ = 3/16 , and p₄ = 1/16

State the appropriate null and alternative hypotheses.. Are the data from this experiment consistent with Mendel's laws? Use a 0.01 significance level. (Assume that the sample is representative of all such tomato plants.)

a) H₀: p₁ = 9/16 , p₂ = 3/16 , p₃ = 3/16 , p₄ = 1/16 H_a: H₀ is not true.

b) H₀: p₁ ≠ 9/16, p₂ ≠ 3/16, p₃ ≠ 3/16, p₄ ≠ 1/16   H_a: H₀ is not true.

c) H₀: p₁ ≠ 926, p₂ ≠ 288, p₃ ≠ 295, p₄ ≠ 101 H_a: H₀ is not true.

d) H₀: p₁ = 926, p₂ = 288, p₃ = 295, p₄ = 101   H_a: H₀ is not true.

e) H₀: p₁ =1/4 , p₂ =1/4 , p₃ =1/4 , p₄ = 1/4   H_a: H₀ is not true.

2. Find the test statistic and P-value. (Use technology. Round your test statistic to three decimal places and your P-value to four decimal places.)

X²=

P-value=

3. State the conclusion in the problem context.

a) Fail to reject H₀. There is not convincing evidence that the data from this experiment are not consistent with Mendel's laws.

b) Fail to reject H₀. There is convincing evidence that the data from this experiment are not consistent with Mendel's laws.

c) Reject H₀. There is not convincing evidence that the data from this experiment are not consistent with Mendel's laws

d) Reject H₀. There is convincing evidence that the data from this experiment are not consistent with Mendel's laws.

Answer 1

The statistical software output for this problem is :

a) H₀: p₁ = 9/16 , p₂ = 3/16 , p₃ = 3/16 , p₄ = 1/16 H_a: H₀ is not true.

X² = 1.254

P-value = 0.7401

a) Fail to reject H₀. There is not convincing evidence that the data from this experiment are not consistent with Mendel's laws.