Question 1

Which of the following best describes a sampling distribution?

Accepted Answer

A distribution of all possible values of a sample statistic for a given sample size selected from a population.

Question 2

Suppose the population mean is $\mu = 50$ and the population standard deviation is $\sigma = 10$. What is the standard error of the mean for samples of size $n = 25$?

Accepted Answer

$2$

Question 3

If a population is not normally distributed, which theorem allows us to use the normal distribution to approximate the sampling distribution of the sample mean for large sample sizes?

Accepted Answer

Central Limit Theorem

Question 4

A population has $\mu = 100$ and $\sigma = 20$. What is the probability that a sample mean from a sample of $n = 64$ is between $98$ and $102$? (Assume normality.)

Accepted Answer

About $0.3829$

Question 5

Which of the following statements about the standard error of the mean is TRUE?

Accepted Answer

It decreases as the sample size increases.

Question 6

Given a population proportion $\pi = 0.3$ and a sample size $n = 100$, what is the standard error of the sample proportion?

Accepted Answer

$0.0458$

Question 7

A company knows that $40\%$ of its customers prefer online shopping. If a random sample of $200$ customers is selected, what is the probability that the sample proportion is between $0.40$ and $0.45$?

Accepted Answer

$0.4251$

Question 8

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

Accepted Answer

The sample mean $\bar{X}$

Question 9

If the population distribution is normal, what is the shape of the sampling distribution of the sample mean for any sample size $n$?

Accepted Answer

Normal

Question 10

A restaurant has an average wait time of $8$ minutes with a standard deviation of $3$ minutes. For a random sample of $n = 36$ customers, what is the standard error of the mean?

Accepted Answer

$0.5$

Question 11

Suppose you want to find the interval that includes $95\%$ of all sample means for a population with $\mu = 368$, $\sigma = 15$, and $n = 25$. What are the lower and upper limits of this interval?

Accepted Answer

$362.12$ and $373.88$

Question 12

Which of the following conditions must be met for the sampling distribution of the sample proportion to be approximately normal?

Accepted Answer

$n\pi > 5$ and $n(1-\pi) > 5$

Question 13

If the sample size increases, what happens to the variability of the sampling distribution of the sample mean?

Accepted Answer

It decreases.

Question 14

A population has values $18, 20, 22, 24$. What is the mean of this population?

Accepted Answer

$21$

Question 15

Which formula is used to calculate the $Z$-value for a sample mean $\bar{X}$?

Accepted Answer

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

Question 16

A sample of $n = 100$ is taken from a population with $\mu = 500$ and $\sigma = 80$. What is the probability that the sample mean is greater than $516$? (Assume normality.)

Accepted Answer

About $0.0228$

Question 17

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

Accepted Answer

It always has the same standard deviation as the population.

Question 18

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

Accepted Answer

$n > 30$

Question 19

A sample of $n = 49$ is drawn from a population with $\mu = 70$ and $\sigma = 14$. What is the probability that the sample mean is less than $67$?

Accepted Answer

About $0.0668$

Question 20

Which of the following real-world scenarios best illustrates the concept of a sampling distribution?

Accepted Answer

A researcher repeatedly samples groups of 50 patients from a hospital and records the mean blood pressure for each group.

Sampling Distributions: Concepts and Applications in Business Statistics

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