Q1. In a survey of 1152 adults in the United States, 207 said they would be likely to buy an EV. Identify the population and the sample. Describe the sample data.

Background

Topic: Populations and Samples

This question tests your understanding of the difference between a population (the entire group of interest) and a sample (a subset of that group), as well as how to describe sample data.

Key Terms:

• Population: The complete set of individuals or items being studied.

• Sample: A subset of the population, selected for study.

• Sample Data: The information collected from the sample.

Step-by-Step Guidance

1. Identify the group that the survey is intended to represent. Think about who the "population" is in this context.

2. Determine which individuals actually participated in the survey. This is your "sample."

3. Describe what information was collected from the sample. What does the number 207 represent?

4. Consider how the sample data could be used to make inferences about the population.

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Q2. Determine whether each number describes a population parameter or a sample statistic. Explain your reasoning.

• (a) Based on a survey of 2798 U.S. households, it is estimated that the average weekly grocery store spend by a U.S. household is $165.

• (b) The freshman class at a university has an average SAT math score of 514.

• (c) In a random check of several hundred retail stores, the Food and Drug Administration found that 34% of the stores were not storing fish at the proper temperature.

• (d) Last year, a small company spent a total of $5,150,694 on employees’ salaries.

• (e) In the United States, a survey of about 17,000 individuals aged 15 and over found that 14% of them provided unpaid eldercare.

Background

Topic: Parameters vs. Statistics

This question tests your ability to distinguish between a parameter (a value describing a population) and a statistic (a value describing a sample).

Key Terms:

• Parameter: A numerical summary of a population.

• Statistic: A numerical summary of a sample.

Step-by-Step Guidance

1. For each item, identify whether the value is based on the entire population or just a sample.

2. If the value is based on a survey or a subset, it is likely a statistic. If it is based on all members of a group, it is likely a parameter.

3. Explain your reasoning for each item, focusing on whether the data comes from a sample or the whole population.

4. For each, decide if it is a parameter or a statistic, but stop before stating the final classification for all items.

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Q3. For each study, identify the population and the sample. Then determine which part of the study represents the descriptive branch of statistics. What conclusions might be drawn from the study using inferential statistics?

• (a) A study of 1000 U.S. adults who relocated in the last five years found that the average cost in the U.S. to move locally is $1692, and the average cost to move long distance is $4401.

• (b) In a study of 1541 U.S. workers, 39% said they worry that if they told their employer about a mental health condition, it would have a negative impact on them in the workplace.

Background

Topic: Descriptive vs. Inferential Statistics

This question tests your ability to distinguish between descriptive statistics (summarizing sample data) and inferential statistics (drawing conclusions about a population).

Key Terms:

• Descriptive Statistics: Summarizing and displaying data from a sample.

• Inferential Statistics: Using sample data to make generalizations about a population.

Step-by-Step Guidance

1. Identify the population for each study (the group the study aims to learn about).

2. Identify the sample (the group actually studied).

3. Determine which results are descriptive statistics (summaries of the sample data).

4. Think about what kinds of conclusions could be drawn about the population using inferential statistics, based on the sample data.

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Q4. A study asked 2000 U.S. adults, “How long are you willing to wait for a website to load?” Thirty-eight percent of the respondents said 7 to 10 seconds.

• (a) Identify the population and the sample.

• (b) Determine which part of the study represents the descriptive branch of statistics.

• (c) What conclusions might be drawn from the study using inferential statistics?

Background

Topic: Descriptive and Inferential Statistics

This question tests your ability to identify populations and samples, and to distinguish between descriptive and inferential statistics.

Key Terms:

• Population: The entire group of interest.

• Sample: The subset surveyed.

• Descriptive Statistics: Summarizing sample data.

• Inferential Statistics: Drawing conclusions about the population.

Step-by-Step Guidance

1. Identify the group the study is intended to represent (population).

2. Identify the group actually surveyed (sample).

3. Determine which result is a summary of the sample data (descriptive statistics).

4. Think about what generalizations could be made about the population (inferential statistics).

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Q5. The table shows a partial list of vulnerable, endangered, or critically endangered species and the approximate numbers of each species remaining. Which data are qualitative data? Which are quantitative data? Explain your reasoning.

Background

Topic: Qualitative vs. Quantitative Data

This question tests your ability to distinguish between qualitative (categorical) and quantitative (numerical) data.

Key Terms:

• Qualitative Data: Non-numerical, descriptive data (e.g., names, categories).

• Quantitative Data: Numerical data (e.g., counts, measurements).

Step-by-Step Guidance

1. Look at the table and identify which columns contain names or categories (qualitative).

2. Identify which columns contain numbers representing counts or measurements (quantitative).

3. Explain why each type of data fits its classification.

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Q6. The populations of several U.S. cities are shown in the table. Which data are qualitative data? Which are quantitative data? Explain your reasoning.

Background

Topic: Qualitative vs. Quantitative Data

This question tests your ability to classify data as qualitative or quantitative.

Key Terms:

• Qualitative Data: Descriptive, non-numerical data.

• Quantitative Data: Numerical data.

Step-by-Step Guidance

1. Identify which column contains names or categories (qualitative).

2. Identify which column contains numbers (quantitative).

3. Explain your reasoning for each classification.

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Q7. Determine whether each data set is nominal or ordinal.

• Top Five Fastest-Growing U.S. Occupations: Wind turbine service technicians, Nurse practitioners, Data scientists, Statisticians, Information security analysts

• Movie Genres: Action, Adventure, Comedy, Drama, Horror

Background

Topic: Levels of Measurement

This question tests your ability to distinguish between nominal (categorical, no order) and ordinal (ordered) data.

Key Terms:

• Nominal: Data can be categorized but not ordered.

• Ordinal: Data can be categorized and ordered.

Step-by-Step Guidance

1. For each data set, ask whether the entries can be meaningfully ordered.

2. If the data are just categories with no order, they are nominal.

3. If the data are ranked or ordered, they are ordinal.

4. Explain your reasoning for each set.

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Q8. Determine whether each data set is nominal or ordinal.

• (a) WNBA Western Conference final standings.

• (b) A list of phone numbers.

Background

Topic: Levels of Measurement

This question tests your ability to classify data as nominal or ordinal.

Key Terms:

• Nominal: Categories only, no order.

• Ordinal: Categories with order.

Step-by-Step Guidance

1. For each data set, consider whether the entries can be ordered.

2. If the data are just labels, they are nominal.

3. If the data are ranked, they are ordinal.

4. Explain your reasoning for each.

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Q9. Two data sets are shown below. Which data set consists of data at the interval level? Which data set consists of data at the ratio level? Explain your reasoning.

• New York Yankees’ World Series victories (years): 1923, 1927, ...

• 2023 American League home run totals (by team): Baltimore 183, Boston 182, ...

Background

Topic: Levels of Measurement – Interval vs. Ratio

This question tests your ability to distinguish between interval (arbitrary zero, differences meaningful) and ratio (true zero, ratios meaningful) levels of measurement.

Key Terms:

• Interval: Quantitative, differences meaningful, no true zero.

• Ratio: Quantitative, differences and ratios meaningful, true zero.

Step-by-Step Guidance

1. For each data set, consider whether zero means the absence of the quantity.

2. Ask if ratios (e.g., twice as many) are meaningful.

3. Determine which set is interval and which is ratio, but stop before stating the final classification.

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Q10. For each data set, determine whether the data are at the interval level or at the ratio level. Explain your reasoning.

• (a) The body temperatures, in degrees Fahrenheit, of an athlete during an exercise session.

• (b) The heart rates, in beats per minute, of an athlete during an exercise session.

Background

Topic: Levels of Measurement – Interval vs. Ratio

This question tests your ability to classify data as interval or ratio level.

Key Terms:

• Interval: Quantitative, no true zero.

• Ratio: Quantitative, true zero.

Step-by-Step Guidance

1. For each data set, consider whether zero means the absence of the quantity.

2. Ask if ratios are meaningful (e.g., twice as much).

3. Explain your reasoning for each.

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Q11. Complete the table below to summarize which operations are meaningful at each of the four levels of measurement. When identifying a data set’s level of measurement, use the highest level that applies.

Background

Topic: Levels of Measurement

This question tests your understanding of which mathematical operations are meaningful at each level of measurement.

Key Terms:

• Nominal: Categories only.

• Ordinal: Categories and order.

• Interval: Categories, order, differences.

• Ratio: Categories, order, differences, ratios.

Step-by-Step Guidance

1. For each level, consider which operations are meaningful.

2. Fill in the table with check marks or yes/no for each operation, but stop before completing the entire table.

3. Use the highest level that applies when classifying data.

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Q12. Determine whether each study is an observational study or an experiment.

• (a) Researchers study the effect of vitamin D3 supplementation among patients who were newly diagnosed with a viral infection. To perform the study, researchers give 2700 U.S. adults either a daily vitamin D3 supplement or a placebo for four weeks.

• (b) To assess how confident people are in the U.S. economy, researchers call 1019 U.S. adults. They ask them to rate current U.S. economic conditions and whether the U.S. economy is getting better or worse.

• (c) A study used information found in the public domain to make associations between playing different sports and lifespan.

• (d) A survey showed that more than a third of people who say they have a sense of smell disorder have experienced one or more gas safety scares in the last five years.

Background

Topic: Observational Study vs. Experiment

This question tests your ability to distinguish between studies where a treatment is applied (experiment) and studies where data is simply observed (observational).

Key Terms:

• Observational Study: No treatment applied; data observed.

• Experiment: Treatment applied; responses measured.

Step-by-Step Guidance

1. For each study, ask whether a treatment was applied or if data was just observed.

2. If subjects are assigned to groups and receive a treatment, it's an experiment.

3. If no treatment is applied, it's observational.

4. Explain your reasoning for each.

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Q13. A company wants to test the effectiveness of a new gum developed to help people quit smoking. Identify a potential problem with each experimental design and suggest a way to improve it.

• (a) The company identifies ten adults who smoke heavily. Five subjects are given the gum and the other five are given a placebo. After two months, the subjects are evaluated, and it is found that the subjects using the gum have quit smoking.

• (b) The company identifies 1000 adults who smoke heavily. The subjects are divided into blocks according to age. The gum is given to subjects who are 18–39 years old. A placebo is given to those who are over 39 years old. After two months, a significant number of the subjects who are 18–39 years old have quit smoking.

Background

Topic: Experimental Design and Bias

This question tests your ability to identify flaws in experimental design and suggest improvements.

Key Terms:

• Bias: Systematic error favoring certain results.

• Randomization: Assigning subjects randomly to groups.

• Confounding Variable: A variable that affects the outcome and is not controlled.

Step-by-Step Guidance

1. For each design, identify any issues such as small sample size, lack of randomization, or confounding variables.

2. Suggest a method to improve the design, such as increasing sample size or randomizing group assignment.

3. Explain why your suggestion would reduce bias or confounding.

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Q14. A company identifies 240 adults who smoke heavily. The subjects are randomly assigned to either a gum treatment group or a control group. Each subject also watches a video about the dangers of smoking. After four months, most subjects in the treatment group have quit smoking. Identify a potential problem with the experimental design and suggest a way to improve it.

Background

Topic: Experimental Design and Confounding Variables

This question tests your ability to identify confounding variables and suggest improvements to experimental design.

Key Terms:

• Confounding Variable: A variable that affects the outcome and is not controlled.

• Control Group: Group that does not receive the treatment.

Step-by-Step Guidance

1. Identify any factors besides the gum that could influence quitting smoking.

2. Consider whether both groups received the same additional intervention (the video).

3. Suggest a way to improve the design to isolate the effect of the gum.

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Q15. A college has 731 first-year students. Describe how you could choose a simple random sample of eight students for a study.

Background

Topic: Sampling Techniques – Simple Random Sample

This question tests your understanding of how to select a simple random sample.

Key Terms:

• Simple Random Sample: Every possible sample has an equal chance of being selected.

Step-by-Step Guidance

1. Assign a unique number to each student from 1 to 731.

2. Use a random number generator or draw numbers from a hat to select eight unique numbers.

3. Select the students whose numbers were chosen.

4. Ensure each student had an equal chance of being selected.

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Q16. Suppose you want to survey residents of Rhode Island about the effect of artificial intelligence (AI) on job security. How would you select a sample using Stratified Sampling?

Background

Topic: Sampling Techniques – Stratified Sample

This question tests your understanding of stratified sampling, which involves dividing the population into groups (strata) and sampling from each group.

Key Terms:

• Stratum (plural: strata): A subgroup of the population with similar characteristics.

• Stratified Sample: Randomly select members from each stratum.

Step-by-Step Guidance

1. Identify relevant strata (e.g., age, gender, occupation) among Rhode Island residents.

2. Divide the population into these strata.

3. Randomly select a proportional number of residents from each stratum.

4. Combine the selected individuals to form your sample.

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Q17. Suppose you want to survey residents of Rhode Island about the effect of artificial intelligence (AI) on job security. How would you select a sample using Cluster Sampling?

Background

Topic: Sampling Techniques – Cluster Sample

This question tests your understanding of cluster sampling, which involves dividing the population into naturally occurring groups (clusters) and sampling entire clusters.

Key Terms:

• Cluster: A naturally occurring group (e.g., towns, neighborhoods).

• Cluster Sample: Randomly select clusters and survey all members within them.

Step-by-Step Guidance

1. Divide Rhode Island residents into clusters (e.g., by town or city).

2. Randomly select one or more clusters.

3. Survey all residents within the selected clusters.

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Q18. Suppose you want to survey residents of Rhode Island about the effect of artificial intelligence (AI) on job security. How would you select a sample using Systematic Sampling?

Background

Topic: Sampling Techniques – Systematic Sample

This question tests your understanding of systematic sampling, which involves selecting every kth member after a random start.

Key Terms:

• Systematic Sample: Select every kth member after a random starting point.

Step-by-Step Guidance

1. Order or number all Rhode Island residents.

2. Randomly choose a starting point.

3. Select every kth resident after the starting point (e.g., every 10th).

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Q19. You are conducting a study to determine the opinions of students at your school regarding stem cell research. Identify the sampling technique used in each situation. Discuss potential sources of bias, if any.

• (a) You divide the student population according to majors and randomly select and question some students in each major.

• (b) You assign each student a number and generate random numbers. You then question each student whose number is randomly selected.

• (c) You select students who are in your biology class.

• (d) You select a class at random and question each student in the class.

• (e) You assign each student a number and, after choosing a random starting number, question every 25th student.

Background

Topic: Sampling Techniques and Bias

This question tests your ability to identify sampling methods and recognize potential bias.

Key Terms:

• Stratified Sample: Divide into groups, sample from each.

• Simple Random Sample: Random selection from entire population.

• Convenience Sample: Select those easiest to reach.

• Cluster Sample: Randomly select groups, sample all in group.

• Systematic Sample: Select every kth member.

• Bias: Systematic error favoring certain results.

Step-by-Step Guidance

1. For each situation, identify the sampling technique used.

2. Consider whether the method could introduce bias.

3. Explain your reasoning for each.

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