Question 1

Which of the following best describes a population parameter?

Accepted Answer

A numerical descriptive measure of a population, usually unknown.

Question 2

Suppose you toss a fair coin twice and let $$x be $$the number of heads observed. What is the probability that the sample mean $$\bar{x} is$$ $$0.5$$?

Accepted Answer

$$\frac{1}{2}$$

Question 3

Which of the following is an unbiased estimator of the population mean $$\mu$$?

Accepted Answer

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

Question 4

If the sampling distribution of a statistic has a mean equal to the population parameter it estimates, the statistic is said to be:

Accepted Answer

An unbiased estimator

Question 5

Given a population with mean $$\mu = 80$$ and standard deviation $$\sigma = 6$$, a random sample of $$n = 36 is $$taken. What is the standard error of the mean?

Accepted Answer

$$\frac{6}{\sqrt{36}}$$

Question 6

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

Accepted Answer

Approaches a normal distribution

Question 7

Which formula gives the standard deviation of the sampling distribution of the sample mean?

Accepted Answer

$$\frac{\sigma}{\sqrt{n}}$$

Question 8

A sample proportion $$\hat{p} is $$considered approximately normal if:

Accepted Answer

$$np \geq 15$$ and $$n(1-p) \geq 15$$

Question 9

Which of the following statements about the sample mean $$\bar{x} is $$TRUE?

Accepted Answer

Its expected value equals the population mean $$\mu.$$

Question 10

If a population is highly skewed, what is generally required for the sampling distribution of the sample mean to be approximately normal?

Accepted Answer

A larger sample size

Question 11

Which of the following is NOT a property of an unbiased estimator?

Accepted Answer

Its expected value is different from the parameter it estimates.

Question 12

A researcher wants to estimate the proportion of defective items in a large shipment. Which statistic should they use as an estimator for the population proportion $$p$$?

Accepted Answer

Sample proportion $$\hat{p}$$

Question 13

The standard deviation of the sampling distribution of the sample proportion $$\hat{p} is $$given by:

Accepted Answer

$$\sqrt{\frac{p(1-p)}{n}}$$

Question 14

Suppose a population has mean $$\mu = 50$$ and standard deviation $$\sigma = 10. If a $$sample of size $$n = 25 is $$taken, what is the mean and standard deviation of the sampling distribution of the sample mean?

Accepted Answer

Mean: $$50$$, Standard deviation: $$2$$

Question 15

A point estimator is best described as:

Accepted Answer

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

Question 16

In a coin-tossing experiment with two tosses, what is the probability that the sample mean $$\bar{x} is$$ $$1$$?

Accepted Answer

$$\frac{1}{4}$$

Question 17

If the mean of the sampling distribution of a statistic is not equal to the parameter it estimates, the statistic is:

Accepted Answer

Biased

Question 18

Which of the following is TRUE about the Central Limit Theorem?

Accepted Answer

It states that the sampling distribution of the sample mean approaches normality as sample size increases.

Question 19

A sample of size $$n = 100 is $$taken from a population with $$p = 0.2. Is $$the sampling distribution of $$\hat{p}$$ approximately normal?

Accepted Answer

Yes, because $$np = 20$$ and $$n(1-p) = 80$$ are both greater than 15.

Question 20

A hospital administrator wants to estimate the average length of stay for patients. Which statistic should be used as the point estimator for the population mean?

Accepted Answer

Sample mean $$\bar{x}$$

Sampling Distributions, Unbiasedness, and the Central Limit Theorem

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