Question 1

Which of the following best describes the sampling distribution of the sample mean when the population is normal with mean $$\mu$$ and standard deviation $$\sigma$$?

Accepted Answer

It is approximately normal with mean $$\mu$$ and standard deviation $$\sigma/\sqrt{n}.$$

Question 2

Suppose the IQ scores in a population are normally distributed with mean 100 and standard deviation 15. What is the standard deviation of the sampling distribution of the sample mean for samples of size $$n=25$$?

Accepted Answer

$$15/\sqrt{25}$$

Question 3

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

Accepted Answer

It becomes approximately normal.

Question 4

A researcher collects a random sample of 35 pregnant women and finds their mean weight gain is 36.2 pounds. The population mean is 30 pounds with a standard deviation of 12.9 pounds. What is the $$z-$$score for this sample mean?

Accepted Answer

$$z = \frac{36.2 - 30}{12.9/\sqrt{35}}$$

Question 5

Which statement about the mean and standard deviation of the sampling distribution of the sample mean is correct?

Accepted Answer

The mean equals the population mean, and the standard deviation is $$\sigma/\sqrt{n}.$$

Question 6

According to the Central Limit Theorem, what is required for the sampling distribution of the sample mean to be approximately normal?

Accepted Answer

The sample size $$n$$ must be greater than or equal to 30, regardless of population shape.

Question 7

A poll finds that 552 out of 1200 adults plan to work while on summer vacation. What is the sample proportion $$\hat{p}$$?

Accepted Answer

$$\hat{p} = 552/1200$$

Question 8

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

Accepted Answer

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

Question 9

If the population proportion of Americans with hearing trouble is $$p=0.15$$, what is the probability that in a random sample of $$n=120$$ Americans, at most 12% have hearing trouble? Which $$z-$$score formula should be used?

Accepted Answer

$$z = \frac{0.12 - 0.15}{\sqrt{0.15(1-0.15)/120}}$$

Question 10

Which of the following is a correct interpretation of a probability of 0.02 for obtaining a sample mean greater than 110 from a population with mean 100?

Accepted Answer

About 2 out of 100 samples will have a mean greater than 110.

Question 11

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

Accepted Answer

The sample size must be large, typically $$n \geq 30.$$

Question 12

A random sample of 120 Americans who regularly listen to music using headphones results in 26 having hearing trouble. If the population proportion is $$p=0.15$$, what is the sample proportion?

Accepted Answer

$$\hat{p} = 26/120$$

Question 13

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

Accepted Answer

The spread decreases as the sample size increases.

Question 14

Suppose the mean number of people living in a household in the US is 2.9 with a standard deviation of 1.48. For a sample of size $$n=30$$, what is the standard deviation of the sampling distribution of the sample mean?

Accepted Answer

$$1.48/\sqrt{30}$$

Question 15

Which of the following is NOT a property of the sampling distribution of the sample proportion as sample size increases?

Accepted Answer

The mean becomes less accurate.

Question 16

If the population proportion is $$p=0.76$$ and the sample size is $$n=60$$, what is the standard deviation of the sampling distribution of the sample proportion?

Accepted Answer

$$\sqrt{0.76(1-0.76)/60}$$

Question 17

Which scenario best illustrates the Central Limit Theorem?

Accepted Answer

A highly skewed population yields an approximately normal sampling distribution of the mean when $$n is $$large.

Question 18

A sample proportion $$\hat{p} is $$considered unusual if its $$z-$$score is:

Accepted Answer

Greater than 2 or less than -2.

Sampling Distributions: Mean and Proportion (Fundamentals of Statistics, Chapter 8)

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