A genetics experiment involves a population of fruit flies consisting of 3 males

Question

A genetics experiment involves a population of fruit flies consisting of 3 males named Andre, Billy, and Carlos and 1 female named Dana. Assume that two fruit flies are randomly selected with replacement. a. After lsting 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 Proportion of females Probabillty 0.5 Type integers or fractions.) b. Find the mean of the sampling distribution «O (Round to two decimal places as neded.) c. ls the mean of the sampling distribution [from part (b) equal to the population proportion of females? If so, does the mean of the sampling distribution of proportions always equal the population proportion? O A. No, the sample mean is equal to the population proportion of females. These values are not always equal, because proportion is a biased estimator. O 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 he population pro portion of emales. T ese values are always equal because proportion san un lased esti mato. O D. Yes, the sample mean is equal to the population proportion of females. These values are ahways equal, because proportion is a biased estimator

Explanation / Answer

Here we are given that there are 3 males - ABC and 1 female: D

Therefore the proportion of females for each of the samples here could be computed as:

Using the above samples, the probability distribution here is obtained as:

b) The mean of the sampling distribution is computed as:

= 0*(9/16) + 0.5*(6/16) + 1*(1/16) = 0.25

Therefore 0.25 is the required value here.

c) The population proportion is also 0.25 as there is 1 female in total 4 people.

Therefore yes the sample proportion is equal to the population proportion. As proportion is always an unbiased estimator, therefore these values are always equal .

Therefore C is the correct answer here.

Sample AA AB AC AD BA BB BC BD CA CB CC CD DA DB DC DD Proportion of females 0 0 0 0.5 0 0 0 0.5 0 0 0 0.5 0.5 0.5 0.5 1

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