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)

Solutions

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 1 year ago

Next > < Previous

Related Solutions

Prior to 1800 in England, the typical moth of the species Biston betularia(peppered moth) had a...

Prior to 1800 in England, the typical moth of the species Biston betularia(peppered moth) had a light pattern. Dark colored moths were rare. By the late 19th century, the light-colored moths were rare, and the moths with dark patterns were abundant. The cause of this change was hypothesized to be selective predation by birds (JW Tutt, 1896). During the industrial revolution, soot and other wastes from industrial processes killed tree lichens and darkened tree trunks. Thus, prior to the pollution...

The distribution of the number of eggs laid by a certain species of hen during their...

The distribution of the number of eggs laid by a certain species of hen during their breeding period has a mean of 36 eggs with a standard deviation of 18.3. Suppose a group of researchers randomly samples 47 hens of this species, counts the number of eggs laid during their breeding period, and records the sample mean. They repeat this 1,000 times, and build a distribution of sample means. A) What is this distribution called? B) Would you expect the...

Two fair dice are tossed, and (X,Y) denote the number of spots on the first and...

Two fair dice are tossed, and (X,Y) denote the number of spots on the first and on the second dice. Consider two random variables: U = X + Y and W = | X - Y |. A). Derive the distribution of U. List all possible values and evaluate their probabilities. B). Derive the distribution of W. List all possible values and evaluate their probabilities. C). Determine the conditional probability P[6 <= U <= 7 | W <= 1]

A moth species responds to sounds by way of simple reflex arcs connecting each ear to...

A moth species responds to sounds by way of simple reflex arcs connecting each ear to flight control muscles on the opposite side of the body. These arcs include: 1) one sensory neuron connected to the tympanic membrane, 2) an association neuron, and 3) a motor neuron that innervates the flight control muscles. A very low-volume playback of a bat call fails to elicit a response. A louder playback causes the moth to fly in the opposite direction. Explain how temporal summation can explain...

In the peppered moth (Biston betularia), black individuals may be either homozygous (A1A1) or heterozygous (A1A2),...

In the peppered moth (Biston betularia), black individuals may be either homozygous (A1A1) or heterozygous (A1A2), whereas pale gray moths are only homozygous (A2A2). Suppose that in a sample of 250 moths from one locality, 108 are black and 142 are gray. b) Assuming that the locus is in Hardy-Weinberg equilibrium, what are the allele frequencies? Show your work below: c) Under this assumption, what proportion of the sample is heterozygous? What is the number of heterozygotes?

In a particular species of salamander, the skin can either be black or brown. The black...

In a particular species of salamander, the skin can either be black or brown. The black phenotype is recessive to the brown phenotype. Within a population of 1000 salamanders, 640 have the brown phenotype. Calculate the allele frequencies for this population. Show all of your work. How many heterozygotes are there? Make up an environmental change that could occur (not an oil spill or something we’ve talked about, invent your own) that would cause a shift in the allele frequencies....

In a hypothetical species of butterfly, wing spots are controlled by a single locus where BB...

In a hypothetical species of butterfly, wing spots are controlled by a single locus where BB individuals have blue spots, YY individuals have yellow spots, and BY individuals have green spots. Ten years ago, a previous collector randomly collected 1000 butterflies and reported finding 90 blues, 420 greens, and 490 yellows. You collect 40 blues, 320 greens, and 640 yellows. Has there been evolution in this population? If yes, is natural selection involved? Explain and justify your answers. This is...

To study genetic variations (i.e. mutations) between species, especially highly divergent species like insects and mammals,...

To study genetic variations (i.e. mutations) between species, especially highly divergent species like insects and mammals, what type of genetic regions or genes have to be used? Give two examples

Some moth species have a very short window of time for mating each year. One year...

Some moth species have a very short window of time for mating each year. One year the moths were breeding during a week when it was breezy and their reproductive success was very low. What is the likely cause of this low success rate? Male moths could not follow the pheromone trails of the females because the wind dispersed the chemicals Female moths could not produce pheromones due to low water availability Female moths did not produce many eggs due...

At a certain black spot, the number of traffic accidents per year follows a Po 10,000)-distribution....

At a certain black spot, the number of traffic accidents per year follows a Po 10,000)-distribution. The number of deaths per accident follows a Po(0.1)-distribution, and the number of casualties per accidents follows a Po(2)-distribution. The correlation coefficient between the number of casualties and the number of deaths per accidents is 0.5. Compute the expectation and variance of the total number of deaths and casualties during a year.

Subjects