Question 1

Which of the following best describes the sampling distribution of the sample mean when the population is normally distributed?

Accepted Answer

It is normally distributed regardless of sample size.

Question 2

Given a population with mean $$\mu = 2.46$$ grams and standard deviation $$\sigma = 0.02$$ grams, what is the standard error of the mean for a sample size $$n = 5$$?

Accepted Answer

$$0.0086$$

Question 3

As the sample size $$n$$ increases, what happens to the standard deviation of the sampling distribution of the sample mean?

Accepted Answer

It decreases.

Question 4

Suppose the weights of pennies are normally distributed with $$\mu = 2.46$$ grams and $$\sigma = 0.02$$ grams. What is the probability that the sample mean of 10 pennies is at least 2.465 grams?

Accepted Answer

0.2148

Question 5

What does the Central Limit Theorem state about the shape of the sampling distribution of the sample mean as sample size increases?

Accepted Answer

It becomes approximately normal regardless of the population distribution.

Question 6

For a fair die, the population mean is $$\mu = 3.5$$ and $$\sigma = 1.708. $$What is the standard error of the mean for a sample size $$n = 10$$?

Accepted Answer

$$0.5409$$

Question 7

If a random sample of 35 oil changes has a mean time less than 11 minutes, what is the Z-score for this sample mean given $$\mu = 11.4$$ and $$\sigma = 3.2$$?

Accepted Answer

$$-0.74$$

Question 8

Which condition must be met for the sampling distribution of the sample proportion $$\hat{p} to be $$approximately normal?

Accepted Answer

$$np(1-p) \geq 10$$

Question 9

In a poll, 349 out of 1745 voters approve of a policy. What is the sample proportion $$\hat{p}$$?

Accepted Answer

$$0.2$$

Question 10

For a population proportion $$p = 0.42$$ and sample size $$n = 50$$, what is the standard deviation of the sampling distribution of $$\hat{p}$$?

Accepted Answer

$$0.0698$$

Question 11

If $$n = 90$$, $$p = 0.188$$, what is the probability that at least 19% of school-aged children are overweight? (Use $$Z = 0.0485)$$

Accepted Answer

0.4801

Question 12

If a sample of 90 children results in 24 overweight children, what is the sample proportion $$\hat{p}$$?

Accepted Answer

$$0.2667$$

Question 13

Which of the following is true about the mean of the sampling distribution of the sample mean?

Accepted Answer

It equals the mean of the parent population.

Question 14

What is the formula for the standard deviation of the sampling distribution of the sample mean?

Accepted Answer

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

Question 15

For a sample proportion $$\hat{p}$$, what is the formula for its standard deviation?

Accepted Answer

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

Question 16

If the sample size is less than 5% of the population, what does this imply about the independence assumption?

Accepted Answer

The sampled values are considered independent.

Question 17

Which histogram would you expect to be most symmetric and bell-shaped: sample means from n=4, n=10, or n=30 from a nonnormal population?

Accepted Answer

n = 30

Question 18

If the population distribution is not normal, what happens to the sampling distribution of the sample mean as n increases?

Accepted Answer

It becomes approximately normal.

Question 19

Which of the following is NOT a requirement for the sampling distribution of the sample proportion to be approximately normal?

Accepted Answer

Sample proportion must equal population proportion.

Question 20

If the sample size increases from n=10 to n=100, what happens to the standard deviation of the sampling distribution of the sample proportion?

Accepted Answer

It decreases.

Sampling Distributions: Sample Means and Proportions

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