Step-by-Step Guidance for Statistics Review Exercises

Study Guide - Smart Notes

Tailored notes based on your materials, expanded with key definitions, examples, and context.

Q1. What term describes a survey where only those who choose to respond are included, and what is wrong with this sampling method?

Background

Topic: Types of Sampling Methods and Bias

This question tests your understanding of voluntary response samples and the potential biases that can result from them.

Key Terms:

Voluntary Response Sample: A sample where participants choose themselves whether to respond.
Bias: A systematic error introduced by the sampling method.

Step-by-Step Guidance

Identify the sampling method used: Consider how the participants were selected (did they volunteer, were they randomly chosen, etc.).
Recall the term for a sample where people opt in to participate.
Think about why this method might not represent the entire population accurately. What kind of people are more likely to respond?
Consider how this could affect the results and what type of bias might be introduced.

Try solving on your own before revealing the answer!

Q2. What is wrong with the survey about who should pay for the first date? Is the 85% value a statistic or a parameter? Is this an experiment or an observational study?

Background

Topic: Survey Design, Statistics vs. Parameters, Types of Studies

This question checks your understanding of survey bias, the difference between statistics and parameters, and the distinction between experiments and observational studies.

Key Terms:

Statistic: A numerical value describing a sample.
Parameter: A numerical value describing a population.
Observational Study: Observing subjects without intervention.
Experiment: Applying a treatment and observing effects.

Step-by-Step Guidance

Analyze how the survey participants were selected. Was it random, or did people choose to respond?
Think about what could be wrong with the way the survey was conducted (e.g., voluntary response bias).
Determine whether the 85% value describes a sample or the entire population. Recall the definitions of statistic and parameter.
Decide if the survey involved any intervention or treatment, or if it simply recorded responses.

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Q3. In a study where 150 patients were treated with oxygen and 148 with a placebo, what do 'randomized' and 'double-blind' mean?

Background

Topic: Experimental Design

This question tests your understanding of key concepts in experimental design, specifically randomization and blinding.

Key Terms:

Randomized: Assignment of subjects to groups by chance.
Double-blind: Neither the subjects nor the experimenters know who receives the treatment or placebo.

Step-by-Step Guidance

Define what it means for a study to be randomized in the context of assigning treatments.
Explain why randomization is important for reducing bias.
Describe what double-blind means in this context.
Discuss how double-blinding helps ensure the validity of the results.

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Q4. If there is a high correlation between divorce rate in Maine and margarine consumption in the US, can we conclude that one causes the other?

Background

Topic: Correlation vs. Causation

This question tests your understanding of the difference between correlation and causation.

Key Terms:

Correlation: A statistical relationship between two variables.
Causation: One variable directly affects another.

Step-by-Step Guidance

Recall the definition of correlation and what it measures.
Consider whether a high correlation alone is enough to establish a cause-and-effect relationship.
Think about possible explanations for the observed correlation (e.g., coincidence, lurking variables).

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Q5. For each scenario, identify the type of sample: systematic, convenience, stratified, cluster, or simple random sample.

Background

Topic: Sampling Methods

This question tests your ability to distinguish between different sampling techniques.

Key Terms:

Systematic Sample: Selecting every k-th item.
Convenience Sample: Using subjects that are easy to reach.
Stratified Sample: Dividing the population into groups and sampling from each group.
Cluster Sample: Dividing the population into clusters, then randomly selecting clusters and using all members from those clusters.
Simple Random Sample: Every member has an equal chance of being selected.

Step-by-Step Guidance

For each scenario, identify how the sample is being selected (e.g., by interval, by group, by convenience, etc.).
Match the description to the correct sampling method based on the definitions above.
Consider whether the sample is random, systematic, stratified, cluster, or convenience for each case.

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Q6. Do differences in wording between two similar questions about the Defense of Marriage Act affect responses?

Background

Topic: Survey Design and Wording Effects

This question examines how question wording can influence survey responses.

Key Terms:

Wording Effect: The impact that the phrasing of a question can have on survey results.

Step-by-Step Guidance

Compare the two questions and note the differences in wording.
Think about how each version might influence a respondent's answer.
Consider why survey designers need to be careful with question wording.

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Q7. Are state population sizes discrete or continuous? What is the level of measurement for the number of residents? What is wrong with mailing questionnaires to 10,000 randomly selected residents? What type of sample is obtained by selecting 50 full-time workers in each state? What type of sample is obtained by selecting two states and surveying all their residents?

Background

Topic: Types of Data, Levels of Measurement, Sampling Methods

This question covers the classification of data, levels of measurement, and sampling techniques.

Key Terms:

Discrete Data: Data that can only take specific values (usually counts).
Continuous Data: Data that can take any value within a range.
Levels of Measurement: Nominal, Ordinal, Interval, Ratio.
Sampling Methods: Random, Systematic, Convenience, Stratified, Cluster.

Step-by-Step Guidance

Decide if the number of residents can be fractional or only whole numbers (discrete vs. continuous).
Recall the definitions of the four levels of measurement and determine which applies to population counts.
Think about potential issues with using mailed questionnaires (e.g., nonresponse bias).
For the sampling scenarios, match the description to the correct sampling method.

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Q8. What is wrong with the claim that U-Turn protein bars contain '125% less fat' than leading chocolate candy brands?

Background

Topic: Interpreting Percentages

This question tests your ability to critically evaluate percentage claims in advertising.

Key Terms:

Percentages: A way to express a number as a fraction of 100.

Step-by-Step Guidance

Recall what it means to have '100% less' of something.
Consider whether it is possible to have '125% less' of a quantity.
Think about how this claim could be misleading or mathematically incorrect.

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Q9. In a Pew Research Center poll, 58% of 1182 respondents said they like to drive. What is the actual number of respondents who said they like to drive?

Background

Topic: Calculating Counts from Percentages

This question tests your ability to convert a percentage into a count using the sample size.

Key Formula:

Remember to convert the percentage to a decimal before multiplying.

Step-by-Step Guidance

Convert 58% to a decimal by dividing by 100.
Multiply the decimal by the total number of respondents (1182).

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Q10. In a Pew Research Center poll, 331 of 1182 respondents said driving is a chore. What percentage of respondents said this?

Background

Topic: Calculating Percentages from Counts

This question tests your ability to convert a count into a percentage of the total.

Key Formula:

Step-by-Step Guidance

Divide the number of respondents who said driving is a chore (331) by the total number of respondents (1182).
Multiply the result by 100 to convert it to a percentage.

Try solving on your own before revealing the answer!

Q11. For each scenario, identify the level of measurement (nominal, ordinal, interval, ratio) and the type of sampling (random, systematic, convenience, stratified, cluster).

Background

Topic: Levels of Measurement and Sampling Methods

This question tests your ability to classify data and sampling techniques.

Key Terms:

Nominal: Categories with no order.
Ordinal: Categories with a meaningful order.
Interval: Ordered, equal intervals, no true zero.
Ratio: Ordered, equal intervals, true zero.
Sampling Methods: Random, Systematic, Convenience, Stratified, Cluster.

Step-by-Step Guidance

For each scenario, identify what is being measured and how (e.g., temperature, party affiliation, movie rating).
Recall the definitions of the four levels of measurement and decide which applies.
Determine the sampling method used in each scenario based on how the sample was selected.