R1. Is the 62% who plan to return next month a population parameter?

Background

Topic: Populations vs. Samples; Parameters vs. Statistics

This question tests your understanding of the difference between a population parameter and a sample statistic in business statistics.

Key Terms:

• Population: The entire group of interest (all loyalty members).

• Sample: A subset of the population (the 80 surveyed members).

• Parameter: A value that describes a characteristic of the population.

• Statistic: A value calculated from the sample data.

Step-by-Step Guidance

1. Identify whether the 62% is calculated from the entire population or just the sample.

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

3. Consider the context: Was the survey conducted among all 2,000 members or only a subset?

4. Think about which term (parameter or statistic) applies to the 62% value.

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R2. Bar chart vs. histogram: Why are bars separated or touching?

Background

Topic: Data Display Types

This question tests your understanding of the difference between bar charts and histograms, and why their bars are formatted differently.

Key Terms:

• Bar Chart: Used for categorical data; bars are separated.

• Histogram: Used for quantitative data; bars touch to show continuous intervals.

Step-by-Step Guidance

1. Recall what type of data each chart is used for: bar charts (categorical), histograms (quantitative).

2. Think about why bar chart bars are separated (distinct categories).

3. Consider why histogram bars touch (adjacent intervals).

4. Check if the statement correctly describes these differences.

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R3. Why use median and IQR for a right-skewed salary distribution?

Background

Topic: Measures of Center and Spread; Resistance to Outliers

This question tests your understanding of why certain summary statistics are preferred for skewed distributions.

Key Terms:

• Median: The middle value; resistant to extreme values.

• IQR (Interquartile Range): Spread of the middle 50% of data; resistant to outliers.

• Right-skewed: Distribution with a long tail to the right (high values).

Step-by-Step Guidance

1. Recall what happens to the mean and standard deviation when there are extreme high values.

2. Think about how the median and IQR respond to outliers compared to the mean and standard deviation.

3. Consider why a compensation analyst would prefer median and IQR for right-skewed data.

4. Check if the statement correctly explains the reason for using these measures.

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R4. If a retailer adds $10 to every transaction, does the mean increase by $10?

Background

Topic: Effects of Linear Transformations on Summary Statistics

This question tests your understanding of how adding a constant to all data values affects the mean.

Key Terms:

• Mean: Average value of all transactions.

• Linear Transformation: Adding or multiplying all values by a constant.

Step-by-Step Guidance

1. Recall the formula for the mean: .

2. Think about what happens if you add $10x_i$.

3. Write the new mean formula: .

4. Expand the sum and see how the mean changes.

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R5. If defect measurements are multiplied by 10, does the standard deviation multiply by 10?

Background

Topic: Effects of Scaling on Spread Measures

This question tests your understanding of how multiplying all data values by a constant affects the standard deviation.

Key Terms:

• Standard Deviation (): Measures spread around the mean.

• Scaling: Multiplying all values by a constant.

Step-by-Step Guidance

1. Recall the formula for standard deviation: .

2. Think about what happens if every is multiplied by $10$.

3. Write the new formula: .

4. Check if the statement matches this result.

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R6. Is sampling employees from every department cluster sampling?

Background

Topic: Sampling Methods

This question tests your understanding of cluster sampling versus other sampling methods.

Key Terms:

• Cluster Sampling: Randomly selecting entire groups (clusters) and sampling all members within them.

• Stratified Sampling: Randomly sampling within each group (stratum).

Step-by-Step Guidance

1. Identify whether the sample is taken from all departments or just some.

2. Recall that cluster sampling involves selecting entire groups, while stratified sampling involves sampling within each group.

3. Check if the method described matches cluster or stratified sampling.

4. Think about which sampling method is used here.

Try solving on your own before revealing the answer!