Question 1

Which of the following best describes a parameter in statistics?

Accepted Answer

A number that reflects properties of a population and is typically an unknown constant.

Question 2

Suppose you want to estimate the average height of all adult males in a country. Why do you use a sample statistic as a point estimate for the population mean?

Accepted Answer

Because collecting data from the entire population is often impractical, and the sample statistic provides an estimate.

Question 3

What is the margin of error in the context of parameter estimation?

Accepted Answer

A measure of how much the sample statistic is expected to vary from the population parameter.

Question 4

Which of the following statements about the sampling distribution of the sample mean is TRUE?

Accepted Answer

Its mean is equal to the population mean.

Question 5

Given a population with mean $$\mu$$ and standard deviation $$\sigma$$, what is the standard error of the sample mean for a sample of size $$n$$?

Accepted Answer

$$\sigma / \sqrt{n}$$

Question 6

A researcher collects 1000 samples of size $$n=30$$ from a non-normal population. What does the Central Limit Theorem predict about the distribution of the sample means?

Accepted Answer

It will be approximately normal.

Question 7

If the standard deviation of a population is $$1.48$$ and the sample size is $$n=4$$, what is the approximate standard error of the sample mean?

Accepted Answer

$$1.48 / \sqrt{4} = 0.74$$

Question 8

Which of the following is a correct application of the Central Limit Theorem?

Accepted Answer

For any population, the distribution of the sample mean is normal if the sample size is large enough.

Question 9

A basketball coach takes five samples of size $$n=6$$ and five samples of size $$n=100$$ from the same population. What is expected about the variability of the sample means?

Accepted Answer

Sample means from $$n=100$$ will have less variability than those from $$n=6.$$

Question 10

Suppose $$X is a $$random variable with mean $$\mu$$ and variance $$\$$sigma^2$$. What is the expected value of the sample mean $$\overline{X}$$ for a sample of size n$?

Accepted Answer

$$E(\overline{X}) = \mu$$

Question 11

If a population is not normal, what sample size is generally considered sufficient for the sampling distribution of the sample mean to be approximately normal?

Accepted Answer

$$n \geq 30$$

Question 12

Given a normal population with $$\mu = 105$$ and $$\sigma = 16$$, what is the probability that the sample mean of a sample of size $$n=20$$ falls between $$103.2$$ and $$106.8$$?

Accepted Answer

$$0.383$$

Question 13

For a population with $$\mu = 18$$ and $$\sigma = 5$$, what is the standard error of the sample mean for $$n = 45$$?

Accepted Answer

$$5 / \sqrt{45} \approx 0.75$$

Question 14

Which of the following steps is NOT part of constructing a sampling distribution for a statistic?

Accepted Answer

Calculate the population mean directly from the sample.

Question 15

If $$\overline{X} is $$the sample mean, $$\mu is $$the population mean, and $$\sigma is $$the population standard deviation, what is the Z-transform for the sample mean?

Accepted Answer

$$Z = \frac{\overline{X} - \mu}{\sigma / \sqrt{n}}$$

Question 16

A survey reports that 41% ± 2.9% of the public believe young adults are having the toughest time in today's economy. What does the ± 2.9% represent?

Accepted Answer

The margin of error at a specified confidence level.

Question 17

If the population distribution is highly skewed, what happens to the sampling distribution of the sample mean as the sample size increases?

Accepted Answer

It becomes approximately normal as sample size increases.

Question 18

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

Accepted Answer

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

Lecture 24: Estimating Parameters, Sampling Distributions, and the Central Limit Theorem

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