Practice: Populations and Samples

1) True or False

1. A parameter is a numerical summary of a sample.

2. A statistic is a numerical summary of a population.

3. The goal of inferential statistics is to use sample statistics to make informed guesses about population parameters.

4. If you survey every single member of a population, the mean value you calculate is a statistic.

5. A population can be thought of as the entire group of individuals or objects about which you want to draw conclusions.

6. If a statistic is a biased estimator, its sampling distribution will be centered exactly on the true population parameter.

7. Systematic errors are also known as bias because they consistently push estimates in the same direction, either too high or too low.

8. Increasing the sample size will reduce the effect of random sampling error.

9. Bias in a study can be reduced by using a larger sample size.

10. The sampling distribution of a statistic is the distribution of the population from which the samples were drawn.

11. The standard deviation of the empirical distribution of a statistic is called the standard error.

12. Selection bias is when your process of measuring a variable systematically misses the target in one direction.

13. If there is non-response bias in a sample, the final sample size for which there is full data is less than the initial sample size

14. The empirical distribution is the observed distribution of the population.

15. The size of the population doesn’t impact the accuracy of the confidence intervals, as long as the sample is small compared to the population.

Show answers

1. False

2. False

3. True

4. False (this would be a parameter)

5. True

6. False

7. True

8. True

9. False

10. False

11. False

12. False. This is Measurement bias.

13. True

14. False. The empirical distribution is the observed distribution of the data at hand. Put another way: it is the distribution of a sample from the population.

15. True

2) Multiple Choice

1. A large online retailer wants to estimate the average spending per customer in the last year. They take a random sample of 5,000 customers and find the average spending to be $250. Which of the following is the population in this study?

   1. The 5,000 customers selected.
   2. The average spending of $250.
   3. All customers of the online retailer.
   4. The total sales of the retailer.

2. A government agency reports that the average weight of all newborn babies in a particular country is 7.5 pounds. This value is a:

   1. Sample
   2. Parameter
   3. Statistic
   4. Variable

3. A researcher wants to know the average height of all university students in a specific country. They measure the height of 100 randomly selected students. What is the average height of these 100 students?

   1. A parameter
   2. The population
   3. A statistic
   4. The sampling distribution

4. A survey on student happiness at a university is sent to students via an optional email link. What type of bias is most likely to occur?

   1. Measurement bias
   2. Selection bias
   3. Interviewer bias
   4. Funding bias

5. A temperature gauge consistently reads 2 degrees higher than the actual temperature. This is an example of:

   1. Random error
   2. Chance variation
   3. Systematic error (bias)
   4. Sampling variation

6. A polling company uses a list of registered landline phone numbers to survey voters. This might result in which type of bias?

   1. Response bias
   2. Selection bias
   3. Observer bias
   4. Recall bias

7. Which of the following is a key way to reduce the variability of a sample statistic?

   1. Use a biased estimator.
   2. Increase the sample size.
   3. Use a smaller population.
   4. Use a less precise measurement tool.

Show answers

1. Option iii. This is the entire group the study is interested in.

2. Option ii. It describes a characteristic of the entire population of newborn babies.

3. Option iii. It is a value calculated from the sample of 100 students.

4. Optional ii. The students who choose to respond may have different opinions about happiness than those who do not.

5. Option iii. The error is consistent and predictable.

6. Option iv. The sample does not represent the entire population of voters, as it excludes those without a landline phone.

7. Option ii. A larger sample size leads to a sampling distribution with less spread (less variability).