Step-by-Step Guidance for STAT 152.1002 Test 1 Review Guide

Q1. Determine whether the data described below are qualitative or quantitative and explain why. The salaries of all state governors

Background

Topic: Types of Data (Qualitative vs. Quantitative)

This question tests your understanding of the difference between qualitative (categorical) and quantitative (numerical) data.

Key Terms:

• Qualitative data: Describes qualities or categories, not measured with numbers.

• Quantitative data: Consists of numerical values that represent counts or measurements.

Step-by-Step Guidance

1. Consider what "salaries" represent: Are they numbers that can be measured or counted, or are they categories or labels?

2. Recall that quantitative data involves numbers that can be used in mathematical operations (like addition or averaging).

3. Think about whether you could calculate the average or total of these data values.

4. Decide if the data are qualitative or quantitative based on your reasoning above.

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Q2. State whether the data described below are discrete or continuous, and explain why. The exact distances (in centimeters) between the chairs in a college classroom

Background

Topic: Discrete vs. Continuous Data

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

Key Terms:

• Discrete data: Can only take specific, separate values (often counts).

• Continuous data: Can take any value within a given range (often measurements).

Step-by-Step Guidance

1. Ask yourself: Can the distance between chairs be measured to any level of precision (e.g., 100.1 cm, 100.12 cm, etc.)?

2. Consider whether the data can take on any value within an interval, or only specific values.

3. Recall that measurements (like length, weight, time) are usually continuous.

4. Decide if the data are discrete or continuous based on your reasoning.

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Q3. Determine whether the given value is a statistic or a parameter. A homeowner measured the voltage supplied to his home on 37 random days, and the average (mean) value is 124.4 volts.

Background

Topic: Statistics vs. Parameters

This question tests your understanding of the difference between a statistic (from a sample) and a parameter (from a population).

Key Terms:

• Statistic: A numerical summary calculated from a sample.

• Parameter: A numerical summary calculated from an entire population.

Step-by-Step Guidance

1. Identify whether the data (37 days) represent a sample or the entire population (all days in a year).

2. Recall that a statistic describes a sample, while a parameter describes a population.

3. Decide if the mean voltage is a statistic or a parameter based on your identification above.

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Q4. State whether the data described below are discrete or continuous, and explain why. The weights (in tons) of the trees in a forest

Background

Topic: Discrete vs. Continuous Data

This question tests your ability to classify data as discrete or continuous.

Key Terms:

• Discrete data: Data that can only take specific, separate values (often counts).

• Continuous data: Data that can take any value within a range (often measurements).

Step-by-Step Guidance

1. Consider whether the weight of a tree can be measured to any level of precision (e.g., 2.1 tons, 2.15 tons, etc.).

2. Ask yourself if the data can take on any value within an interval, or only specific values.

3. Recall that measurements like weight are usually continuous.

4. Decide if the data are discrete or continuous based on your reasoning.

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Q5. Identify the type of sampling used (random, systematic, convenience, stratified, or cluster sampling) in the situation described below. A researcher selects every 546th social security number and surveys the corresponding person.

Background

Topic: Sampling Methods

This question tests your understanding of different sampling techniques used in statistics.

Key Terms:

• Random sampling: Every member of the population has an equal chance of being selected.

• Systematic sampling: Selecting every k-th member from a list or sequence.

• Convenience sampling: Selecting individuals who are easiest to reach.

• Stratified sampling: Dividing the population into subgroups (strata) and sampling from each.

• Cluster sampling: Dividing the population into clusters, then randomly selecting entire clusters.

Step-by-Step Guidance

1. Identify the method used: Is the researcher selecting individuals at regular intervals (e.g., every 546th)?

2. Recall the definition of systematic sampling and compare it to the method described.

3. Eliminate other sampling methods that do not fit the description.

4. Choose the sampling method that matches the process described.

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Q6. Identify which type of sampling is used: random, systematic, convenience, stratified, or cluster. To determine customer opinion of their service, Business Depot randomly selects 90 stores during a certain week and surveys all customers present in the store.

Background

Topic: Sampling Methods

This question tests your ability to identify cluster sampling and distinguish it from other sampling methods.

Key Terms:

• Cluster sampling: The population is divided into groups (clusters), some clusters are randomly selected, and all members of those clusters are surveyed.

Step-by-Step Guidance

1. Notice that entire stores (clusters) are randomly selected, and then all customers in those stores are surveyed.

2. Recall the definition of cluster sampling and compare it to the process described.

3. Eliminate other sampling methods that do not involve surveying all members of selected groups.

4. Choose the sampling method that matches the description.

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Q7. Identify which of these types of sampling is used: random, systematic, convenience, stratified, or cluster. To determine her blood sugar level, Denise divides up her day into three parts: morning, afternoon, and evening. She then measures her blood sugar level at 2 randomly selected times during each part of the day.

Background

Topic: Sampling Methods

This question tests your understanding of stratified sampling.

Key Terms:

• Stratified sampling: The population is divided into subgroups (strata) and random samples are taken from each stratum.

Step-by-Step Guidance

1. Identify the subgroups (morning, afternoon, evening) as strata.

2. Notice that random samples are taken from each stratum.

3. Recall the definition of stratified sampling and compare it to the process described.

4. Eliminate other sampling methods that do not involve dividing into strata and sampling from each.

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