Question

In: Statistics and Probability

In a certain species of moth, there are two variations in the number of black spots...

In a certain species of moth, there are two variations in the number of black spots on the wings, either 2 or 4, which appear to be the result of a single gene.

Scientists hypothesize that 4 spots is dominant to two spots. They cross two individuals that appear to be heterozygous for this trait and 140 offspring are produced.

If 4 spots is in fact dominant:

1. how many would be expected to display 4 spots?

2. how many would be expected to display 2 spots?

What they observed was that 95 of the offspring have 4 spots and 45 have 2 spots. They ask you to use a chi-square test to determine if these results support their hypothesis. Remember , the null hypothesis is that 4 spots is dominant to 2 spots.

3. How many classes (outcomes) are there?

4. Calculate the chi-square. X² =

5. How many degrees of freedom are there?

6. Use the table below. What is the critical value if we use a p of .05?

7. Based on your calculated X² value and the critical value you determined would you reject the null hypothesis? (yes or no)

8. Are four spots dominant to two spots? (yes or no)

Expert Solution

There are 140 offsprings and since 4 spots is the dominant one, we expect a 3:1 ratio since hetrozygous individuals re crossed.

1. We expect 140*3/4=105 would be expected to display 4 spots.

2. There would be 140*1/4=35 two expected to have two spots.

Null Hypothesis: 4 spots is dominant to two spots.

Alternative :4 spots is not dominant

3. There are two outcomes. 4 spots and 2 spots

4. Chi square:

Phenotype	Observed	Expected Proportion	Exp. Frequency	(O-E)
4 spot	95	0.75	105	-10	100	0.952381
2 spot	45	0.25	35	10	100	2.857143
Total	140					3.809524

The calculated value of is therefore 3.8095.

5. There will be 2-1=1 degree of freedom

6. The critial value of

7. Since the calculated value <the critical value, I will not be rejecting the null hypothesis.:NO

8. Are four spots dominant to two spots? Yes

orchestra answered 2 years ago

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