Question

# a. What is the standard error of a sampling distribution? (out of the following) the mean,...

a. What is the standard error of a sampling distribution? (out of the following)

the mean, the probability, the bias, the standard deviation, or the variance

b. What is the standard deviation of a sampling distribution called? (out of the following)

the spread, the variance, the standard error, the mean, the standard variance

c. List two unbiased estimators and their corresponding parameters. (Select all that apply out of the following.)

μ is an unbiased estimator for x-bar, p is an unbiased estimator for p̂, p̂ is an unbiased estimator for p, σ is an unbiased estimator for σx-bar, x-bar is an unbiased estimator for μ, σx-bar is an unbiased estimator for σ

d. Describe how the variability of the distribution changes as the sample size increases. (out of the following)

As the sample size increases, the variability decreases.--It cannot be determined.--- As the sample size increases, the variability stays the same.----As the sample size increases, the variability increases.

e. Suppose x has a distribution with μ = 59 and σ = 14.

1) If random samples of size n = 16 are selected, can we say anything about the x-bar distribution of sample means? (out of the following)

Yes, the x-bar distribution is normal with mean μ x-bar = 59 and σ x-bar = 0.9.------Yes, the x distribution is normal with mean μ x-bar = 59 and σ x-bar = 14.--------Yes, the x-bar distribution is normal with mean μ x-bar = 59 and σ x-bar = 3.5.-----No, the sample size is too small.

2) If the original x distribution is normal, can we say anything about the x-bar distribution of random samples of size 16? (out of the following)

Yes, the x-bar distribution is normal with mean μ x-bar = 59 and σ x-bar = 0.9.--------Yes, the x-bar distribution is normal with mean μ x-bar = 59 and σ x-bar = 14.-------No, the sample size is too small.-------Yes, the x-bar distribution is normal with mean μ x-bar = 59 and σ x-bar = 3.5.

3) Find P(55 ≤ x ≤ 60). (Round your answer to four decimal places.)  