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 Andre and 3 females named Carla, and Diana. Assume that two fruit files are randomly selected with replacement. a After listing the possible samples and finding the proportion of females in each sample, use a table to describe the sampling distribution of the proportion of females. (Type integers or fractions) b. Find the mean of the sampling distribution. mu = (Round to two decimal places as needed.) c.Is the mean of the sampling distribution (from part equal to the population proportion of 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 females. These valves are always equal, because proportion is an estimator. B. No, the sample mean is equal to the population proportion of females. These values are not always equal because proportion is an unbiased estimator. C. Yes, the sample mean is equal to the population proportion of females. These values are always equal, because proportion is a biased estimator ? D. No, the sample mean is equal to the population proportion of females. These values are not always equal, because proportion is a biased estimator.

Explanation / Answer

Assume the name of the fruit flies by the initials.

Here the sample space is

{aa, ab, ac, ad, ba, bb, bc, bd, ca, cb, cc, cd, da, db, dc, dd}

P(0) = 1/16

P(0.5) = 6/16

P(1) = 9/16

mean = 0 * 1/16 + 0.5 * 6/16 + 1 * 9/16

= 0.75

c)

yes , the sample mean is equal to population proportion of females . these values are not always equal because proportion is a biased estimator

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