Q: A random sample of 400 Americans finds that 120 support a new policy. Construct a 95% confidence interval for the population proportion. Use $$z^* = 1.96.$$

$$0.3 \pm 1.96 \times \sqrt{\frac{0.3 \times 0.7}{400}}$$

Q: A random sample of 1000 voters is taken from a population where $$p = 0.5. $$What is the standard error of the sample proportion?

$$\sqrt{\frac{0.5 \times 0.5}{1000}} = 0.0158$$

Question 1

Which of the following best describes the difference between a parameter and a statistic?

Accepted Answer

A parameter is a numerical value that describes a population, while a statistic describes a sample.

Question 2

A researcher wants to estimate the proportion of college students who own a pet. She surveys 500 randomly selected students and finds that 210 own a pet. What is the sample proportion ($$\hat{p}$$)?

Accepted Answer

$$\hat{p} = \frac{210}{500} = 0.42$$

Question 3

Which of the following is an example of sampling bias?

Accepted Answer

Surveying only people who are easy to reach, such as your friends.

Question 4

A survey asks, 'Do you support the unfair tax burden on hardworking citizens?' What type of bias is most likely present?

Accepted Answer

Measurement bias due to non-neutral wording

Question 5

Suppose a population proportion is $$p = 0.3$$ and a simple random sample of size $$n = 100 is $$taken. What is the expected value (mean) of the sample proportion $$\hat{p}$$?

Accepted Answer

$$0.3$$

Question 6

Which of the following conditions must be met to use the Central Limit Theorem for sample proportions?

Accepted Answer

The sample must be randomly selected, the sample size must be large enough (at least 10 successes and 10 failures), and the population must be at least 10 times the sample size.

Question 7

A random sample of 400 Americans finds that 120 support a new policy. Construct a 95% confidence interval for the population proportion. Use $$z^* = 1.96.$$

Accepted Answer

$$0.3 \pm 1.96 	imes \sqrt{\frac{0.3 	imes 0.7}{400}}$$

Question 8

If a 95% confidence interval for a population proportion is (0.45, 0.55), which of the following is a correct interpretation?

Accepted Answer

We are 95% confident that the true population proportion is between 0.45 and 0.55.

Question 9

A poll of 2,000 adults finds that 18% say they have seen a ghost. The 95% confidence interval is (0.163, 0.197). Is it plausible that 25% of all adults have seen a ghost?

Accepted Answer

No, because 0.25 is not within the confidence interval.

Question 10

Which of the following statements about margin of error is correct?

Accepted Answer

Increasing the confidence level increases the margin of error.

Question 11

A survey of 715 homeowners finds that 62% believe their homes are not underwater, with a margin of error of 4% at the 95% confidence level. What is the correct confidence interval?

Accepted Answer

58% to 66%

Question 12

Suppose you want to decrease the standard error of your estimate for a population proportion. Which of the following actions will achieve this?

Accepted Answer

Increase the sample size.

Question 13

A random sample of 1000 voters is taken from a population where $$p = 0.5. $$What is the standard error of the sample proportion?

Accepted Answer

$$\sqrt{\frac{0.5 	imes 0.5}{1000}} = 0.0158$$

Question 14

Which of the following is NOT a requirement for using the normal approximation for the sampling distribution of the sample proportion?

Accepted Answer

The sample must be a convenience sample.

Question 15

A poll finds that 38% of 1000 Americans believe in intelligent life on other planets. The 95% confidence interval is (0.35, 0.41). Is it plausible that 40% of Americans believe in intelligent life on other planets?

Accepted Answer

Yes, because 0.40 is within the confidence interval.

Question 16

If a sample proportion $$\hat{p} is 0.25 $$from a sample of 100, what is the estimated standard error?

Accepted Answer

$$\sqrt{\frac{0.25 	imes 0.75}{100}} = 0.0433$$

Chapter 7: Survey Sampling and Inference – Study Notes

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