Question 1

Which of the following best describes the main purpose of randomization in sampling?

Accepted Answer

To protect against both known and unknown sources of bias in the population.

Question 2

A researcher wants to estimate the average income of residents in a city. She divides the city into neighborhoods and randomly selects a few neighborhoods, then surveys every household in those neighborhoods. What sampling method is she using?

Accepted Answer

Cluster sampling

Question 3

Which equation correctly represents the sample mean, using the proper notation?

Accepted Answer

$$\bar{y} = \frac{1}{n} \sum_{i=1}^{n} y_i$$

Question 4

Which of the following is NOT a potential problem with conducting a census?

Accepted Answer

A census always produces unbiased results.

Question 5

In a stratified random sample, what is the main advantage compared to a simple random sample?

Accepted Answer

It reduces sampling variability by sampling within homogeneous subgroups.

Question 6

A survey is conducted at a shopping mall by asking passersby to participate. Which type of bias is most likely to affect the results?

Accepted Answer

Convenience sampling bias

Question 7

Which of the following statements about sample size is correct?

Accepted Answer

The sample size determines the precision of the statistics, not the population size.

Question 8

What is the best way to avoid bias in a sample survey?

Accepted Answer

Select individuals for the sample at random.

Question 9

Which of the following is an example of nonresponse bias?

Accepted Answer

Busy students do not respond to a survey about stress.

Question 10

A statistician uses a random number generator to select 100 students from a list of all students at a university. What is the sampling frame in this scenario?

Accepted Answer

The list of all students at the university

Question 11

Which equation correctly represents the sample standard deviation?

Accepted Answer

$$s = \sqrt{\frac{1}{n-1} \sum_{i=1}^{n} (y_i - \bar{y})^2$}$$

Question 12

Which of the following is a key difference between stratified and cluster sampling?

Accepted Answer

Stratified sampling uses homogeneous groups, while cluster sampling uses heterogeneous groups.

Question 13

A survey about drug use among teenagers uses the term 'e-cigarette' in its questions, but most teenagers refer to them as 'vapes.' Which type of bias could this introduce?

Accepted Answer

Response bias

Question 14

Which of the following is a population parameter, not a sample statistic?

Accepted Answer

$$\mu$$

Question 15

A researcher wants to survey every 10th person on an alphabetical list of employees, starting from a randomly chosen individual. What sampling method is this?

Accepted Answer

Systematic sampling

Question 16

Which of the following best describes sampling variability?

Accepted Answer

The differences between samples drawn at random from the same population.

Question 17

Which of the following is an example of voluntary response bias?

Accepted Answer

An online poll where only people with strong opinions reply.

Question 18

A survey is conducted using random-digit dialing, but only landline numbers are used. Which type of bias is most likely to occur?

Accepted Answer

Undercoverage bias

Question 19

Which of the following is a best practice for designing a valid survey?

Accepted Answer

Pilot-test your survey and use cognitive interviews to ensure clarity.

Question 20

Which equation correctly represents the sample proportion?

Accepted Answer

$$\hat{p} = \frac{x}{n}$$

Sample Surveys and Bias in Statistics: Study Guide

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