Young’s modulus is a quantitative measure of stiffness of an elastic material. Suppose that for aluminum alloy sheets of a particular type, its mean v

Which of the following is true about the sampling distribution of means?
A. Shape of the sampling distribution of means is always the same shape as the population distribution, no matter what the sample size is.
B. Sampling distributions of means are always nearly normal.
C. Sampling distributions of means get closer to normality as the sample size increases.
D. Sampling distribution of the mean is always right skewed since means cannot be smaller than 0.

Which of the following statements about the sampling distribution of the sample mean is incorrect?
(a) The standard deviation of the sampling distribution will decrease as the sample size increases.
(b) The standard deviation of the sampling distribution is a measure of the variability of the sample mean among repeated samples.
(c) The sample mean is an unbiased estimator of the population mean.
(d) The sampling distribution shows how the sample mean will vary in repeated samples.
(e) The sampling distribution shows how the sample was distributed around the sample mean.

Which of the following are possible examples of sampling distributions? (Select all that apply.)
mean trout lengths based on samples of size 5
average SAT score of a sample of high school students
average male height based on samples of size 30
heights of college students at a sampled universit
yall mean trout lengths in a sampled lake

Which of the following is true about sampling distributions?
-Shape of the sampling distribution is always the same shape as the population distribution, no matter what the sample size is.
-Sampling distributions are always nearly normal.
-Sampling distribution of the mean is always right skewed since means cannot be smaller than 0.
-Sampling distributions get closer to normality as the sample size increases.

Resource managers of forest game lands were concerned about the size of the deer and rabbit populations during the winter months in a particular forest. As an estimate of population size, they proposed using the average number of pellet groups for rabbits and deer per 30-foot-square plots. From an aerial photograph, the forest was divided into N= 10,000 30-foot-square grids. A simple random sample of 2 = 500 plots was taken, and the number of pellet groups was observed for rabbits and for deer. The results of this study are summarized in the accompanying table.
a. Estimate ${\displaystyle {\mu }_1,\text{and}{\mu }_2}$, the average number of pellet groups for deer and rabbits, respectively, per 30-foot-square-plots. Place bounds on the errors of estimation.
b. Estimate the difference in the mean size of pellet groups per plot for the two animals, with an appropriate margin of error.
Deer
Sample mean = 2.30
Sample variance = 0.65
Rabbits
Sample mean = 4.52
Sample variance = 0.97

Explain the meaning of assertion that A is an unbiased estimator of $\alpha$