Table of contents

1. Intro to Stats and Collecting Data1h 14m
2. Describing Data with Tables and Graphs1h 55m
3. Describing Data Numerically2h 5m
4. Probability2h 16m
5. Binomial Distribution & Discrete Random Variables3h 6m
6. Normal Distribution and Continuous Random Variables2h 11m
7. Sampling Distributions & Confidence Intervals: Mean3h 23m
8. Sampling Distributions & Confidence Intervals: Proportion1h 12m
- Sampling Distribution of Sample Proportion
  29m
- Confidence Intervals for Population Proportion
  42m
9. Hypothesis Testing for One Sample3h 29m
10. Hypothesis Testing for Two Samples4h 50m
11. Correlation1h 6m
12. Regression1h 50m
13. Chi-Square Tests & Goodness of Fit1h 57m
14. ANOVA1h 57m

2. Describing Data with Tables and Graphs

Visualizing Qualitative vs. Quantitative Data

Statistics

2. Describing Data with Tables and Graphs

Visualizing Qualitative vs. Quantitative Data

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1:42 minutes

Problem 2.3.3

Textbook Question

Ethics There are data showing that smoking is detrimental to good health. Given that people could be helped and lives could be saved by reducing smoking, is it ethical to graph the data in a way that is misleading by exaggerating the health risks of smoking?

Verified step by step guidance

Understand the ethical implications of presenting data: In statistics, it is crucial to present data accurately and without bias. Misleading graphs can distort the interpretation of data, which may lead to unethical outcomes, even if the intention is to promote a positive cause.

Consider the principles of ethical data representation: Ethical data representation involves honesty, transparency, and clarity. Misleading graphs, such as those with manipulated scales or omitted context, violate these principles and can undermine trust in statistical findings.

Evaluate the potential consequences of exaggerating risks: While the goal of reducing smoking is beneficial, exaggerating health risks through misleading graphs could lead to public mistrust in health campaigns or statistical data in general, potentially harming future efforts to promote public health.

Explore alternative approaches: Instead of exaggerating risks, focus on presenting the data accurately and effectively. Use clear and well-designed graphs that highlight the true health risks of smoking without distortion, ensuring the message is both impactful and ethical.

Reflect on professional responsibility: As statisticians or data communicators, it is our responsibility to uphold ethical standards in data presentation. Misleading graphs, even with good intentions, compromise the integrity of the field and the trust of the audience.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Ethical Considerations in Data Presentation

Ethical considerations in data presentation involve the responsibility of researchers and communicators to present data honestly and transparently. Misleading representations can distort public understanding and lead to harmful consequences. In the context of health data, exaggerating risks may induce unnecessary fear or anxiety, while downplaying risks can lead to complacency.

Statistical Misrepresentation

Statistical misrepresentation occurs when data is presented in a way that misleads the audience about the true nature of the information. This can include using inappropriate scales, cherry-picking data, or employing misleading visuals. Understanding how to accurately represent data is crucial for ensuring that the audience receives a truthful interpretation of the findings.

Public Health Implications

Public health implications refer to the potential effects that data presentation can have on community health behaviors and policies. Accurate data can inform effective interventions and promote healthier choices, while misleading data can hinder public health efforts. It is essential to balance the urgency of health messages with ethical data representation to foster informed decision-making.

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Related Practice

Textbook Question

Are Nuclear Plants Safe? Using the survey results from Exercise 2 and ignoring those respondents with no opinion, is the following graph somehow misleading? If so, how?

Textbook Question

You are a member of your local apartment association. The association represents rental housing owners and managers who operate residential rental property throughout the greater metropolitan area. Recently, the association has received several complaints from tenants in a particular area of the city who feel that their monthly rental fees are much higher compared to other parts of the city.

You want to investigate the rental fees. You gather the data shown in the table at the right. Area A represents the area of the city where tenants are unhappy about their monthly rents. The data represent the monthly rents paid by a random sample of tenants in Area A and three other areas of similar size. Assume all the apartments represented are approximately the same size with the same amenities.

a. What type of graph would you choose to display the data? Explain your reasoning.

Multiple Choice

Use the frequency distribution below to find the class width and class midpoints.

Multiple Choice

The following data set shows the number of overtime hours that 12 employees worked in a month. Construct a frequency distribution, suing a lower class limit of 3 and a class width of 4.

Textbook Question

Finding the Best Model

In Exercises 5–16, construct a scatterplot and identify the mathematical model that best fits the given data. Assume that the model is to be used only for the scope of the given data, and consider only linear, quadratic, logarithmic, exponential, and power models.

Dirt Cheap The Cherry Hill Construction company in Branford, CT sells screened topsoil by the “yard,” which is actually a cubic yard. Let the variable x be the length (yd) of each side of a cube of screened topsoil. The table below lists the values of x along with the corresponding cost (dollars).

Textbook Question

Finding the Best Model

Sound Intensity The table lists intensities of sounds as multiples of a basic reference sound. A scale similar to the decibel scale is used to measure the sound intensity.

Textbook Question

In Exercises 1 and 2, use the following wait times (minutes) at 10:00 AM for the Tower of Terror ride at Disney World (from Data Set 33 “Disney World Wait Times” in Appendix B).

35 35 20 50 95 75 45 50 30 35 30 30

d. The accompanying normal quantile plot is obtained by using all 50 wait times at 10:00 AM for the Tower of Terror ride at Disney World. Based on this normal quantile plot, do the sample data appear to be from a normally distributed population?

Textbook Question

In Exercises 1 and 2, use the following wait times (minutes) at 10:00 AM for the Tower of Terror ride at Disney World (from Data Set 33 “Disney World Wait Times” in Appendix B).

35 35 20 50 95 75 45 50 30 35 30 30

b. Construct a boxplot.

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