Table of contents
- 1. Intro to Stats and Collecting Data55m
- 2. Describing Data with Tables and Graphs1h 55m
- 3. Describing Data Numerically1h 45m
- 4. Probability2h 16m
- 5. Binomial Distribution & Discrete Random Variables2h 33m
- 6. Normal Distribution and Continuous Random Variables1h 38m
- 7. Sampling Distributions & Confidence Intervals: Mean1h 3m
- 8. Sampling Distributions & Confidence Intervals: Proportion1h 12m
- 9. Hypothesis Testing for One Sample1h 1m
- 10. Hypothesis Testing for Two Samples2h 8m
- 11. Correlation48m
- 12. Regression1h 4m
- 13. Chi-Square Tests & Goodness of Fit1h 20m
- 14. ANOVA1h 0m
1. Intro to Stats and Collecting Data
Intro to Stats
Problem 1.R.8.a
Textbook Question
Percentages
a. The labels on U-Turn protein energy bars include the statement that these bars contain “125% less fat than the leading chocolate candy brands†(based on data from Consumer Reports magazine). What is wrong with that claim?

1
Understand the concept of percentage reduction: A percentage reduction is calculated as the difference between the original and new values, divided by the original value, then multiplied by 100 to convert it to a percentage.
Recognize the logical flaw: A claim of '125% less fat' implies that the energy bars have negative fat content, which is not possible. Percentages over 100% in this context are nonsensical because they suggest a reduction greater than the total amount present.
Consider the correct interpretation: A more accurate claim would be that the energy bars have a certain percentage of the fat content of the leading chocolate candy brands, such as '75% less fat' if they contain 25% of the original fat content.
Evaluate the claim mathematically: If the leading chocolate candy brand has X grams of fat, a 125% reduction would imply the energy bars have X - 1.25X = -0.25X grams of fat, which is impossible.
Conclude with the correct approach: The claim should be revised to reflect a realistic and mathematically sound percentage reduction, ensuring it does not exceed 100%.

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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Understanding Percentages
Percentages are a way to express a number as a fraction of 100, often used to compare proportions. When a claim states '125% less,' it implies a reduction greater than the original amount, which is mathematically impossible. Understanding how percentages work is crucial to identifying errors in such claims.
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Step 1: Write Hypotheses
Interpreting Percentage Reductions
A percentage reduction indicates how much a quantity decreases relative to its original value. A claim of '125% less' suggests a complete reduction and then some, which is nonsensical. Typically, reductions are expressed as a percentage of the original, not exceeding 100%.
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Step 1: Write Hypotheses
Misleading Advertising Claims
Misleading claims often use percentages to exaggerate benefits or differences. In this case, the claim of '125% less fat' is misleading because it suggests an impossible reduction. Recognizing such tactics is important for critically evaluating product information and advertisements.
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Step 1: Write Hypotheses Example 1
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