Question

A genetics experiment involves a population of fruit flies consisting of 1 male named Bart and 3 females named Charlene, Diana, and Erin. 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.
Proportion of males Probability
0 [ ]
0.5 [ ]
1 [ ]
(Type integers or fractions)
b. Find the mean of the sampling distribution
= [ ] (Round to two decimal places as needed)
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. No, the sample mean is equal to the population proportion of males. These values are not always equal, because proportion is a biased estimator.
B. No, the sample mean is equal to the population proportion of males. These values are not always equal, because proportion is an unbiased estimator.
C. Yes, the sample mean is equal to the population proportion of males. These values are always equal, because proportion is an unbiased estimator.
D. Yes, the sample mean is equal to the population proportion of males. These values are always equal, because proportion is a biased estimator

Answer 1

Answer:

(b) [TeX] \frac{1}{2}[/TeX]

Step-by-step explanation:

1 male named Bart (b)

3 females named Charlene(c), Diana(d), and Erin(e).

Since there is replacement, the possible samples are:

bb, bc, be, bd, cb, cc, cd, ce, db, dc, dd, de, eb, ec, ed, and ee.

Total Number of pairs = 16

Event of picking 2 males:bb

Event of 1 male:bc,cb,bd,db,be,eb

Event of picking 0 males:

cc, cd, ce, dc, dd, de, ec, ed, and ee.

[TeX]  \begin{equation*} \begin{matrix}Proportion of males & Probability \\0 & 9/16 \\1 & 6/16 \\2 & 1/16 \end{matrix} \end{equation*} [/TeX]

b. The mean of the sampling distribution

[TeX] \mu = (\frac{9}{16} X0 ) +(\frac{6}{16} X 1)+(\frac{1}{16} X 2) = \frac{8}{16} = \frac{1}{2} [/TeX]

c.  No; the proportion of males is [TeX] \frac{1}{4}[/TeX] while the mean is [TeX] \frac{1}{2}[/TeX].

B. No, the sample mean is not equal to the population proportion of males. These values are not always equal, because proportion is an unbiased estimator.