A genetics experiment involves a population of fruit flies consisting of 1 male

Question

A genetics experiment involves a population of fruit flies consisting of 1 male named Christopher and 3 females named Diana, Emily, and Fran. Assume that two fruit flies are randomly selected with replacement. a. After listing the possible samples and finding the proportion of males in each sample, use a table to describe the sampling distribution of the proportion of males. (Type integers or fractions.) b. Find the mean of the sampling distribution. mu = c. Is the mean of the sampling distribution [from part (b)] equal to the population proportion of males? If so, does the mean of the sampling distribution of proportions always equal the population proportion? A. Yes, the sample mean is equal to the population proportion of males. These values are always equal, because proportion is a biased estimator. B. Yes, the sample mean is equal to the population proportion of males. These values are always equal, because proportion is an unbiased estimator. C. No, the sample mean is equal to the population proportion of males. These values are not always equal, because proportion is an unbiased estimator. D. No, the sample mean is equal to the population proportion of males. These values are not always equal, because proportion is a biased estimator.

Explanation / Answer

Answers to the question:

a.

prop 0 males - 3C2/4C2 = .5

prop .5 male - 1*3C1/4C2 = .5

prop 1 male - 0 ( as there is 1 male and 2 are needed0

b. Mean = 0*.5+.5*.5+1*0 = .25

c. The sample mean is a random variable that is an estimator of the population mean. The expected value of the sample mean is equal to the population mean µ. Therefore, the sample meanis an unbiased estimator of the population mean.

Given 1 male, 3 females, prob that a person selected is man is .25.

When 2 are samples, then it leads to sample mean of .25 ( Same as above - pop. proportion mean)

So, B is the answer.

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