Ch. 4 - Probability

Triola - Elementary Statistics 14th Edition

Triola14th EditionElementary StatisticsISBN: 9780137366446Not the one you use?Change textbook

Triola 14th Edition

Ch. 4 - Probability

Problem 4.CRE.5

Chapter 4, Problem 4.CRE.5

Heights of Presidents Theories have been developed about the heights of winning candidates for the U.S. presidency and the heights of candidates who were runners up. Listed below are heights (cm) from recent presidential elections. Construct a graph suitable for exploring an association between heights of presidents and the heights of the presidential candidates who were runners-up. What does the graph suggest about that association?

Verified step by step guidance

Step 1: Identify the type of graph suitable for exploring the association between the heights of winners and runners-up. A scatter plot is ideal for visualizing the relationship between two numerical variables, such as the heights of winners and runners-up.

Step 2: Label the axes of the scatter plot. The x-axis can represent the heights of the winners (in cm), and the y-axis can represent the heights of the runners-up (in cm). This ensures clarity in interpreting the graph.

Step 3: Plot the data points on the scatter plot. For each pair of heights (winner and runner-up), plot a point where the x-coordinate corresponds to the winner's height and the y-coordinate corresponds to the runner-up's height. For example, the first pair (182, 180) would be plotted as (182, 180).

Step 4: Analyze the pattern of the points on the scatter plot. Look for trends, such as whether the points tend to cluster along a diagonal line, which would suggest a positive association between the heights of winners and runners-up.

Step 5: Interpret the graph. If the points show a clear trend (e.g., taller winners tend to have taller runners-up), this suggests a positive association. If the points are scattered without a clear pattern, it suggests no strong association between the heights of winners and runners-up.

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Key Concepts

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

Scatter Plot

A scatter plot is a graphical representation used to display the relationship between two quantitative variables. In this context, it can be used to plot the heights of winning presidential candidates against the heights of their runners-up. Each point on the graph represents a pair of heights, allowing for visual assessment of any correlation or trend between the two sets of data.

Correlation

Correlation measures the strength and direction of a linear relationship between two variables. In this case, it helps to determine whether taller winning candidates tend to have taller or shorter runners-up. A positive correlation would suggest that as the height of winners increases, so does the height of runners-up, while a negative correlation would indicate the opposite.

Descriptive Statistics

Descriptive statistics summarize and describe the main features of a dataset. For the heights of presidents and their runners-up, measures such as mean, median, and range can provide insights into the overall height trends. Understanding these statistics is essential for interpreting the data accurately and making informed conclusions about the association between the two groups.

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In Exercises 6–10, use the following results from tests of an experiment to test the effectiveness of an experimental vaccine for children (based on data from USA Today). Express all probabilities in decimal form.

Find the probability of randomly selecting 2 subjects without replacement and finding that they both developed flu.

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Cloud Seeding The “Florida Area Cumulus Experiment” was conducted by using silver iodide to seed clouds with the objective of increasing rainfall. For the purposes of this exercise, let the daily amounts of rainfall be represented by units of rnfl. (The actual rainfall amounts are in or )

Find the value of the following statistics and include appropriate units based on rnfl as the unit of measurement.

15.53 7.27 7.45 10.39 4.70 4.50 3.44 5.70 8.24 7.30 4.05 4.46

a. mean

b. median

Textbook Question

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a. A statistics instructor collects eye color data from her students. What is the name for this type of sample?

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Textbook Question

Find the value of the following statistics and include appropriate units based on rnfl as the unit of measurement.

[Image]

c. midrange

d. range

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Textbook Question

In Exercises 1–10, use the data in the accompanying table and express all results in decimal form. (The data are from “The Left-Handed: Their Sinister History,” by Elaine Fowler Costas, Education Resources Information Center, Paper 399519.)

Lefty or Female Find the probability of randomly selecting one of the study subjects and getting someone who writes with their left hand or is a female.

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In Exercises 9–20, use the data in the following table, which lists survey results from high school drivers at least 16 years of age (based on data from “Texting While Driving and Other Risky Motor Vehicle Behaviors Among U.S. High School Students,” by O’Malley, Shults, and Eaton, Pediatrics, Vol. 131, No. 6). Assume that subjects are randomly selected from those included in the table. Hint: Be very careful to read the question correctly.

Texting or Drinking If one of the high school drivers is randomly selected, find the probability of getting one who texted while driving or drove when drinking alcohol.

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