A genetics experiment involves a population of fruit flies consisting of 3 males named Christian, Denny, and Ernie and 1 female named Fran. Assume that two fruit flies 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.
Proportions of females Probability
0 ...
0.5 ...
1 ...
fill the table
b. Find the mean of the sampling distribution.
c. Is 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?
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.
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 an unbiased estimator.

To determine the sampling distribution of the proportion of females in the population of fruit flies, we can list all of the possible samples of two fruit flies that can be drawn with replacement.

Now according to the question we have, Proportions of females Probability

0 (3/4)² = 9/16

0.5 (1/4 * 3/4) + (3/4 * 1/4) = 6/16

1 (1/4)² = 1/16

So, the sampling distribution of the proportion of females in the population is as follows:

Proportions of females Probability

0 9/16

0.5 6/16

1 1/16

b. To find the mean of the sampling distribution, we can multiply each proportion by its probability and add up the results:

(0 * 9/16) + (0.5 * 6/16) + (1 * 1/16) = 3/8

So, the mean of the sampling distribution is 3/8.

c. No, the mean of the sampling distribution is not equal to the population proportion of females, which is 1/4. The mean of the sampling distribution is an estimate of the population proportion, but it is not always equal to the population proportion. The mean of the sampling distribution can be either higher or lower than the population proportion, depending on the specific values and probabilities in the sampling distribution. In general, the mean of the sampling distribution of proportions is an unbiased estimator of the population proportion, meaning that it is expected to be close to the true population proportion on average, but it is not always equal to the population proportion.

Learn more about Probability at:

brainly.com/question/25870256

#SPJ4