Which of the following is true about sampling distributions? -Shape of the sampling distribution is always the same shape as the population distributi

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 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.

To identify:An important assumption for using the bootstrap method

Check whether the standard error of the sampling distributions of $\bar{p}$ obtained in part(a) and part(b) are different.

The Wall Street Journal reported that the age at first startup for $55\mathrm{\%}$ of entrepreneurs was 29 years of age or less and the age at first startup for $45\mathrm{\%}$ of entrepreneurs was 30 years of age or more.
a. Suppose a sample of 200 entrepreneurs will be taken to learn about the most important qualities of entrepreneurs. Show the sampling distribution of $\bar{p}$ where $\bar{p}$ is the sample proportion of entrepreneurs whose first startup was at 29 years of age or less.
b. Suppose a sample of 200 entrepreneurs will be taken to learn about the most important qualities of entrepreneurs. Show the sampling distribution of $\bar{p}$ where $\bar{p}$ is now the sample proportion of entrepreneurs whose first startup was at 30 years of age or more.
c. Are the standard errors of the sampling distributions different in parts (a) and (b)?