Textbook Question
ESP A psychologist tells you that in an ESP (extrasensory perception) experiment, there is a 20% chance of answering a question correctly. What is the probability of answering a question correctly?
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Ch. 4 - Probability
Triola14th EditionElementary StatisticsISBN: 9780137366446
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Table of contents
- Ch. 1 - Introduction to Statistics88
- Ch. 2 - Exploring Data with Tables and Graphs70
- Ch. 3 - Describing, Exploring, and Comparing Data66
- Ch. 4 - Probability112
- Ch. 5 - Discrete Probability Distributions109
- Ch. 6 - Normal Probability Distributions122
- Ch. 7 - Estimating Parameters and Determining Sample Sizes107
- Ch. 8 - Hypothesis Testing75
- Ch. 9 - Inferences from Two Samples94
- Ch. 10 - Correlation and Regression80
- Ch. 11 - Goodness-of-Fit and Contingency Tables29
- Ch. 12 - Analysis of Variance42
Chapter 4, Problem 4.q.6
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.
If 1 of the 1602 subjects is randomly selected, find the probability of getting 1 that developed flu.
Verified step by step guidance1
Step 1: Begin by identifying the total number of subjects in the experiment. Add all the values in the table: 14 (Developed Flu, Vaccine Treatment) + 1056 (Did Not Develop Flu, Vaccine Treatment) + 95 (Developed Flu, Placebo) + 437 (Did Not Develop Flu, Placebo).
Step 2: Calculate the total number of subjects who developed flu. Add the values from the 'Developed Flu' column: 14 (Vaccine Treatment) + 95 (Placebo).
Step 3: To find the probability of randomly selecting a subject who developed flu, divide the total number of subjects who developed flu (from Step 2) by the total number of subjects in the experiment (from Step 1).
Step 4: Express the probability as a decimal. Ensure the division result is rounded appropriately if necessary.
Step 5: Interpret the result. The probability represents the likelihood of randomly selecting a subject who developed flu from the entire group of 1602 subjects.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Probability
Probability is a measure of the likelihood that a particular event will occur, expressed as a number between 0 and 1. In this context, it refers to the chance of randomly selecting a subject who developed the flu from the total number of subjects. The probability can be calculated by dividing the number of favorable outcomes (subjects who developed flu) by the total number of outcomes (total subjects).
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Experimental Design
Experimental design refers to the framework for conducting an experiment, including how subjects are assigned to treatment groups. In this case, the subjects are divided into two groups: those receiving the vaccine treatment and those receiving a placebo. Understanding the design helps in interpreting the results and assessing the effectiveness of the vaccine.
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Contingency Table
A contingency table is a data representation that displays the frequency distribution of variables, allowing for the analysis of the relationship between them. The provided table shows the number of subjects who developed or did not develop flu under two different treatments (vaccine and placebo). This format aids in calculating probabilities and understanding the impact of the vaccine.
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09:47Finding Standard Normal Probabilities using z-Table
Related Practice
Textbook Question
Standard Tests Standard tests, such as the SAT or ACT or MCAT, tend to make extensive use of multiple-choice questions because they are easy to grade using software. If one such multiple choice question has possible correct answers of a, b, c, d, e, what is the probability of a wrong answer if the answer is a random guess?
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Textbook Question
Vision Correction About 75% of the U.S. population uses some type of vision correction (such as glasses or contact lenses).
d. If you randomly select four people, is a result of all four using vision correction significantly high? Why or why not?
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Textbook Question
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.
If 1 of the 1602 subjects is randomly selected, find the probability of getting 1 who had the vaccine treatment and developed flu.
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Textbook Question
National Statistics Day
b. If a person is randomly selected, find the probability that his or her birthday is in October. Ignore leap years.
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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.)
Complement If L represents the event of randomly selecting one of the study subjects and getting someone who writes with their left hand, what does L represent? Find the value of P(L)
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