Question 1

A researcher wants to estimate the average number of M&Ms in all fun-sized bags. Which of the following best describes the parameter of interest?

Accepted Answer

The mean number of M&Ms in all fun-sized bags ($$\mu)$$

Question 2

Which of the following statements about the Central Limit Theorem (CLT) is correct?

Accepted Answer

The CLT states that the sampling distribution of the sample mean becomes approximately Normal as the sample size increases, regardless of the population's shape.

Question 3

Suppose the population standard deviation is $$\sigma = 12$$ and you take a simple random sample of size $$n = 36. $$What is the standard deviation of the sampling distribution of the sample mean?

Accepted Answer

$$\2$

Question 4

A population is strongly right-skewed. Which of the following is true as the sample size increases?

Accepted Answer

The distribution of the sample means becomes more Normal.

Question 5

Which of the following is NOT a condition for using the Normal model for the sampling distribution of the sample mean?

Accepted Answer

Population must be symmetric

Question 6

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

Accepted Answer

It is always Normal.

Question 7

A sample of CEO compensations is strongly right-skewed. If you take many samples of size $$n = 10$$, what will the shape of the sampling distribution of the sample mean most likely be?

Accepted Answer

Still right-skewed

Question 8

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

Accepted Answer

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

Question 9

A researcher collects a random sample of 50 patients' blood pressure readings from a large hospital. The population distribution is slightly skewed. Which statement is most accurate about the sampling distribution of the sample mean?

Accepted Answer

It will be approximately Normal.

Question 10

Why is it important that the sample size is less than 10% of the population when constructing a confidence interval for the mean?

Accepted Answer

To ensure the independence of observations.

Question 11

A random sample of size $$n = 100 is $$taken from a population with mean $$\mu = 50$$ and standard deviation $$\sigma = 20. $$What is the expected mean and standard deviation of the sampling distribution of the sample mean?

Accepted Answer

Mean: $$50$$, SD: $$2$$

Question 12

Which of the following best describes the effect of increasing sample size on the standard deviation of the sampling distribution of the sample mean?

Accepted Answer

It decreases.

Question 13

A student claims: 'If I take a large enough sample, the sample mean will always equal the population mean.' Is this statement correct?

Accepted Answer

No, the sample mean will be close to the population mean, but not always equal.

Question 14

Which of the following is a real-world example where the Central Limit Theorem is useful?

Accepted Answer

Estimating the average time it takes for a medication to take effect in a large population using a sample.

Question 15

If a population is very skewed, what is a general guideline for the minimum sample size needed for the sampling distribution of the mean to be approximately Normal?

Accepted Answer

$$n \u003e 40$$

Question 16

A sample of size $$n = 25 is $$taken from a population with unknown shape. Which of the following is most likely true about the sampling distribution of the sample mean?

Accepted Answer

It will be approximately Normal if the population is not extremely skewed.

Question 17

Which of the following is the correct interpretation of a 95% confidence interval for the mean number of M&Ms in fun-sized bags?

Accepted Answer

We are 95% confident that the true mean number of M&Ms in all fun-sized bags is within the interval.

Confidence Intervals for Means and the Central Limit Theorem

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