Step-by-Step Guidance for Introduction to Statistics Worksheet

Study Guide - Smart Notes

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

Q1. Does the source in the medical organization example have the potential to create bias in a statistical study?

Background

Topic: Bias in Statistical Studies

This question tests your understanding of how the source of funding or affiliation can introduce bias into a statistical study.

Key Terms:

Bias: A conscious or unconscious predetermined opinion that can affect the outcome of a study.
Source: The origin of the data or funding for the study.

Step-by-Step Guidance

Read the description carefully and identify any affiliations or funding sources mentioned.
Consider whether the organization’s stance or funding could influence the results or interpretation of the study.
Think about how a predetermined opinion or financial interest might affect the objectivity of the research.

Try solving on your own before revealing the answer!

Q2. Does the source in the brain volume study example have the potential to create bias?

Background

Topic: Bias in Statistical Studies

This question asks you to evaluate whether the institutions involved in data collection could introduce bias.

Key Terms:

Bias
Source

Step-by-Step Guidance

Identify the institutions involved in the study.
Consider whether these institutions have any reason to influence the results.
Think about whether the data collection process appears objective or if there is potential for bias.

Try solving on your own before revealing the answer!

Q3. Is the sampling method in the milk survey sound or flawed?

Background

Topic: Sampling Methods

This question tests your ability to identify flaws in sampling methods, specifically voluntary response samples.

Key Terms:

Voluntary Response Sample: Respondents decide whether to be included.
Sampling Method: The process used to select subjects for a study.

Step-by-Step Guidance

Identify how the survey subjects were selected (internet users who responded to a posted question).
Recall the definition of voluntary response sample.
Consider whether this method is likely to produce a representative sample or if it introduces bias.

Try solving on your own before revealing the answer!

Q4. Is the sampling method in the AARP credit card debt survey sound or flawed?

Background

Topic: Sampling Methods

This question asks you to evaluate whether random selection leads to a sound sampling method.

Key Terms:

Random Sample: Each subject has an equal chance of being chosen.
Sampling Method

Step-by-Step Guidance

Identify how the subjects were selected (randomly).
Recall the advantages of random sampling.
Consider whether this method is likely to produce a representative sample.

Try solving on your own before revealing the answer!

Q5. For the survey about senior undergraduate students' emotional readiness, state the population and sample. Is the 70% value a statistic or parameter?

Background

Topic: Population, Sample, Statistic, Parameter

This question tests your understanding of the difference between population and sample, and whether a value is a statistic or parameter.

Key Terms:

Population: Complete collection of all data.
Sample: Subset of population.
Statistic: Measurement based on sample.
Parameter: Measurement based on population.

Step-by-Step Guidance

Identify the population described (all senior undergraduate students).
Identify the sample (if any is mentioned).
Determine whether the 70% value refers to the entire population or just a sample.

Try solving on your own before revealing the answer!

Q6. For the study of American Airlines flights, state the population and sample. Is the average arrival time a statistic or parameter?

Background

Topic: Population, Sample, Statistic, Parameter

This question tests your ability to distinguish between sample and population, and identify statistics versus parameters.

Key Terms:

Population
Sample
Statistic
Parameter

Step-by-Step Guidance

Identify the population (all flights from JFK to LAX).
Identify the sample (48 randomly selected flights).
Determine whether the average arrival time is based on the sample or population.

Try solving on your own before revealing the answer!

Q7. For the homeowner's voltage measurements, state the population and sample. Is the average value a statistic or parameter?

Background

Topic: Population, Sample, Statistic, Parameter

This question tests your understanding of how to classify values as statistics or parameters based on the data collection.

Key Terms:

Population
Sample
Statistic
Parameter

Step-by-Step Guidance

Identify the population (all days in the month).
Identify the sample (all 30 days measured).
Determine whether the average is based on the sample or population.

Try solving on your own before revealing the answer!

Q8. For the Kingman diet study, do the results have statistical significance and practical significance?

Background

Topic: Statistical and Practical Significance

This question tests your ability to distinguish between statistical significance (unlikely to occur by chance) and practical significance (meaningful in real life).

Key Terms:

Statistical Significance: Result is unlikely to occur by chance.
Practical Significance: Result is meaningful or useful in practice.

Step-by-Step Guidance

Identify the average weight loss and the probability of getting such results by chance.
Recall the definitions of statistical and practical significance.
Consider whether the result is both statistically and practically significant.

Try solving on your own before revealing the answer!

Q9. For the birth sex selection study, do the results have statistical significance and practical significance?

Background

Topic: Statistical and Practical Significance

This question tests your ability to interpret statistical results and their practical implications.

Key Terms:

Statistical Significance
Practical Significance

Step-by-Step Guidance

Identify the number of males and females born and the probability of getting such results by chance.
Recall the definitions of statistical and practical significance.
Consider whether the result is both statistically and practically significant.

Try solving on your own before revealing the answer!

Q10. Percentages in TheKnot.com survey: a) What is 48% of 1165 respondents?

Background

Topic: Calculating Percentages

This question tests your ability to calculate the exact value from a percentage of a total.

Key Formula:

Step-by-Step Guidance

Identify the total number of respondents: 1165.
Identify the percentage: 48% (convert to decimal: 0.48).
Set up the calculation:

Try solving on your own before revealing the answer!

Q10b. Could the result from part (a) be the actual number of survey subjects who said a bended knee is essential? Why or why not?

Background

Topic: Percentages and Whole Numbers

This question tests your understanding of whether a percentage calculation always results in a whole number.

Key Terms:

Percentage
Whole Number

Step-by-Step Guidance

Consider whether multiplying a percentage by a total always gives a whole number.
Think about the context: survey responses must be whole people.
Reflect on whether the calculated value from part (a) is a whole number.

Try solving on your own before revealing the answer!

Q10c. What is the actual number of survey respondents saying that the bended knee is essential?

Background

Topic: Rounding Percentages

This question tests your ability to round the calculated value to the nearest whole number.

Key Formula:

Step-by-Step Guidance

Use the value calculated in part (a).
Round the result to the nearest whole number.

Try solving on your own before revealing the answer!

Q10d. What percentage of respondents said that a bended knee is corny and outdated?

Background

Topic: Calculating Percentages

This question tests your ability to calculate the percentage from a count and a total.

Key Formula:

Step-by-Step Guidance

Identify the number of respondents: 93.
Identify the total number of respondents: 1165.
Set up the calculation:

Try solving on your own before revealing the answer!

Q11a. Among the women, what is the exact value of 19% of 1543?

Background

Topic: Calculating Percentages

This question tests your ability to calculate the exact value from a percentage of a total.

Key Formula:

Step-by-Step Guidance

Identify the total number of women: 1543.
Identify the percentage: 19% (convert to decimal: 0.19).
Set up the calculation:

Try solving on your own before revealing the answer!

Q11b. Could the result from part (a) be the actual number of women who responded with “rarely, if ever”? Why or why not?

Background

Topic: Percentages and Whole Numbers

This question tests your understanding of whether a percentage calculation always results in a whole number.

Key Terms:

Percentage
Whole Number

Step-by-Step Guidance

Consider whether multiplying a percentage by a total always gives a whole number.
Think about the context: survey responses must be whole people.
Reflect on whether the calculated value from part (a) is a whole number.

Try solving on your own before revealing the answer!

Q11c. What is the actual number of women who responded with “rarely, if ever”?

Background

Topic: Rounding Percentages

This question tests your ability to round the calculated value to the nearest whole number.

Key Formula:

Step-by-Step Guidance

Use the value calculated in part (a).
Round the result to the nearest whole number.

Try solving on your own before revealing the answer!

Q11d. What percentage of men responded “rarely, if ever”?

Background

Topic: Calculating Percentages

This question tests your ability to calculate the percentage from a count and a total.

Key Formula:

Step-by-Step Guidance

Identify the number of men who responded: 219.
Identify the total number of men: 1458.
Set up the calculation:

Try solving on your own before revealing the answer!

Q12–19. Classify the data as qualitative or quantitative, and as discrete or continuous.

Background

Topic: Types of Data

These questions test your ability to classify data as qualitative (categorical) or quantitative (numerical), and further as discrete (countable) or continuous (measurable).

Key Terms:

Qualitative Data: Categorical data consisting of names or labels.
Quantitative Data: Numerical data consisting of counts or measurements.
Discrete: Finite or countable values.
Continuous: Infinite or uncountable values.

Step-by-Step Guidance

For each item, decide if the data is categorical (qualitative) or numerical (quantitative).
If quantitative, determine if the values are countable (discrete) or measurable (continuous).
Apply the definitions to each example and classify accordingly.

Try classifying each item before revealing the answer!

Q20–21. Is the description an observational study or an experiment?

Background

Topic: Types of Studies

These questions test your ability to distinguish between observational studies (no treatment applied) and experiments (treatment applied).

Key Terms:

Experiment: Treatment is applied, effects are observed.
Observational Study: No treatment, just observation and measurement.

Step-by-Step Guidance

Read the description and identify whether any treatment or intervention is applied.
If treatment is applied, classify as experiment; if not, classify as observational study.
Apply the definitions to each scenario.

Try classifying each item before revealing the answer!

Q22–23. Identify what is wrong in the given statements.

Background

Topic: Common Errors in Statistical Reasoning

These questions test your ability to spot flaws such as biased polls and incorrect assumptions about causation.

Key Terms:

Bias
Correlation vs. Causation

Step-by-Step Guidance

For each statement, identify any potential sources of bias or logical errors.
Recall that correlation does not imply causation.
Think about whether the conclusion is justified based on the data provided.