Question 1

Which of the following best describes a sampling distribution?

Accepted Answer

The probability distribution of all possible values of a sample statistic calculated from repeated samples of the same size from a population.

Question 2

Suppose the population mean $$\mu is 100 $$and the population standard deviation $$\sigma is 20. If $$you take a random sample of size $$n = 25$$, what is the standard error of the sample mean?

Accepted Answer

$$4$$

Question 3

Which property must an estimator have to be considered unbiased?

Accepted Answer

Its expected value equals the population parameter it estimates.

Question 4

According to the Central Limit Theorem, as the sample size $$n$$ increases, the sampling distribution of the sample mean $$\overline{x}$$:

Accepted Answer

Becomes approximately normal, regardless of the population's distribution.

Question 5

If a sample statistic consistently overestimates the population parameter, it is said to be:

Accepted Answer

A biased estimator.

Question 6

Given a population with mean $$\mu = 50$$ and standard deviation $$\sigma = 10$$, what is the probability that the sample mean of a random sample of size $$n = 36 is $$between 48 and 52? (Assume normality.)

Accepted Answer

About 0.9544

Question 7

Which of the following is NOT a property of the sampling distribution of the sample mean?

Accepted Answer

It is always normal, regardless of sample size.

Question 8

A company bottles soda with a mean fill of 12 oz and a standard deviation of 0.2 oz. If a quality control manager samples 50 bottles, what is the standard error of the sample mean?

Accepted Answer

$$0.03$$

Question 9

Which formula correctly expresses the standard error of the sample mean?

Accepted Answer

$$\sigma_{\overline{x}} = \frac{\sigma}{\sqrt{n}}$$

Question 10

If the sample proportion $$\hat{p} is $$used to estimate the population proportion $$p$$, which of the following is true about $$\hat{p}$$ for large sample sizes?

Accepted Answer

The sampling distribution of $$\hat{p} is $$approximately normal.

Question 11

A researcher takes all possible samples of size 2 from a population of 4 values: 1, 2, 3, 4. What is the mean of the sampling distribution of the sample means?

Accepted Answer

2.5

Question 12

Which of the following statements about the Central Limit Theorem is FALSE?

Accepted Answer

It applies only to populations that are normally distributed.

Question 13

If the population standard deviation $$\sigma is $$unknown and the sample size is large, which of the following is the best estimate for the standard error of the mean?

Accepted Answer

$$\frac{s}{\sqrt{n}}$$

Question 14

A point estimator is:

Accepted Answer

A rule or formula that uses sample data to estimate a population parameter.

Question 15

Which of the following is a minimum-variance unbiased estimator (MVUE) for the population mean $$\mu$$?

Accepted Answer

The sample mean $$\overline{x}$$

Sampling Distributions and the Central Limit Theorem

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