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Step-by-Step Guidance for MAT-181 Midterm (Elementary Statistics, Chapters 1-4)

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Q1. A pollster divides a state's voters into urban, suburban, and rural groups and then randomly selects voters from each group. Which sampling method is this?

Background

Topic: Sampling Methods

This question tests your understanding of different sampling methods used in statistics to collect data from a population.

Key Terms:

  • Simple random sample: Every member of the population has an equal chance of being selected.

  • Systematic sample: Select every kth member from a list.

  • Stratified sample: Divide the population into groups (strata) and randomly sample from each group.

  • Cluster sample: Randomly select entire groups and sample all members within those groups.

Step-by-Step Guidance

  1. Identify the process described: The population is divided into groups based on location (urban, suburban, rural).

  2. Notice that random selection occurs within each group, not from the whole population or from entire groups.

  3. Recall the definition of stratified sampling: dividing into strata and sampling from each.

  4. Compare with cluster sampling, where whole groups are selected and all members are surveyed.

Try solving on your own before revealing the answer!

Final Answer: (C) stratified

The pollster divides the population into strata (urban, suburban, rural) and randomly samples from each, which is stratified sampling.

Q2. A researcher randomly selects 8 high schools in a state and surveys every senior in those schools. Which sampling method is this?

Background

Topic: Sampling Methods

This question tests your ability to distinguish between cluster and stratified sampling.

Key Terms:

  • Cluster sample: Randomly select entire groups (clusters) and survey all members within those groups.

  • Stratified sample: Divide into groups and randomly sample from each group.

Step-by-Step Guidance

  1. Identify the process: Random selection of entire schools (clusters).

  2. All seniors in the selected schools are surveyed, not just a random sample from each school.

  3. Recall that cluster sampling involves surveying all members of selected clusters.

  4. Contrast with stratified sampling, where only some members from each group are chosen.

Try solving on your own before revealing the answer!

Final Answer: (D) cluster

Cluster sampling is used because entire schools are selected and all seniors within those schools are surveyed.

Q3. Which variable is measured at the ratio level?

Background

Topic: Levels of Measurement

This question tests your understanding of the four levels of measurement: nominal, ordinal, interval, and ratio.

Key Terms:

  • Ratio level: Has a true zero, meaningful differences, and ratios are meaningful.

  • Interval level: Meaningful differences, no true zero.

  • Ordinal level: Order matters, differences are not meaningful.

  • Nominal level: Names or labels only, no order.

Step-by-Step Guidance

  1. Review each variable: ZIP code, calendar year, minutes studied, letter grade.

  2. Identify which variable has a true zero and allows for meaningful ratios.

  3. Recall that ratio variables can be compared using multiplication/division (e.g., twice as much).

  4. Eliminate variables that are categorical or lack a true zero.

Try solving on your own before revealing the answer!

Final Answer: (C) number of minutes a student studied

This variable is measured at the ratio level because it has a true zero and meaningful ratios.

Q4. A study of 500 adults finds that those who wear fitness trackers weigh less on average. A reporter concludes that trackers cause weight loss. What is the best criticism?

Background

Topic: Observational Studies vs. Experiments

This question tests your ability to recognize confounding variables and the limitations of observational studies.

Key Terms:

  • Observational study: No treatment applied, just observation.

  • Confounding variable: A variable that may affect the outcome and is not controlled for.

  • Correlation vs. causation: Correlation does not imply causation.

Step-by-Step Guidance

  1. Identify the type of study: Was it observational or experimental?

  2. Consider whether other variables could explain the observed difference.

  3. Recall that only experiments with random assignment can establish causation.

  4. Think about confounding variables (e.g., people who wear trackers may also exercise more).

Try solving on your own before revealing the answer!

Final Answer: (B) It was an observational study, so confounding variables may explain the difference.

Observational studies cannot establish causation due to possible confounding variables.

Q5. Which is a discrete quantitative variable?

Background

Topic: Types of Data

This question tests your ability to distinguish between discrete and continuous quantitative variables.

Key Terms:

  • Discrete data: Countable values (e.g., number of patients).

  • Continuous data: Measured on a scale, infinite possible values (e.g., height, time).

Step-by-Step Guidance

  1. Review each option: height, number of patients, blood type, time spent waiting.

  2. Identify which variable can only take whole number values.

  3. Recall that discrete variables are counts, not measurements.

  4. Eliminate variables that are continuous or categorical.

Try solving on your own before revealing the answer!

Final Answer: (B) the number of patients in a waiting room

This is a discrete quantitative variable because it is a countable number.

Q6. A histogram of exam scores has a peak near 85 and a long tail stretching to the left. Which statement is true?

Background

Topic: Distribution Shape and Measures of Center

This question tests your understanding of how skewness affects the mean and median.

Key Terms:

  • Skewed left: Long tail toward smaller values.

  • Mean: Sensitive to outliers and skewness.

  • Median: Resistant to outliers.

Step-by-Step Guidance

  1. Identify the shape: Peak near 85, tail to the left (skewed left).

  2. Recall that in left-skewed distributions, the mean is pulled below the median.

  3. Compare the mean and median in terms of their positions in the distribution.

  4. Eliminate options that do not match the effect of left skew.

Try solving on your own before revealing the answer!

Final Answer: (B) The mean is less than the median.

In a left-skewed distribution, the mean is pulled below the median.

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