Essentials of Statistics (6th Edition)
6th Edition
ISBN: 9780134685779
Author: Mario F. Triola
Publisher: PEARSON
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Textbook Question
Chapter 11, Problem 1FDD
FROM DATA TO DECISION
Critical Thinking: Was Allstate wrong?
The Allstate insurance company once issued a press release listing zodiac signs along with the corresponding numbers of automobile crashes, as shown in the first and last columns in the table below.
In the original press release. Allstate included comments such as one stating that Virgos are worried and shy, and they were involved in 211,650 accidents, making them the worst offenders. Allstate quickly issued an apology and retraction. In a press release. Allstate included this: “Astrological signs have absolutely no role in how we base coverage and set rates. Rating by astrology would not be actuarially sound.”
Analyzing the Results
The original Allstate press release did not include the lengths (days) of the different zodiac signs. The preceding table lists those lengths in the third column. A reasonable explanation for the different numbers of crashes is that they should he proportional to the lengths of the zodiac signs. For example, people are born under the Capricorn sign on 29 days out of the 365 days in the year, so they are expected to have 29/365 of the total number of crashes. Use the methods of this chapter to determine whether this appears to explain the results in the table. Write a brief report of your findings.
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The National Center for Health Statistics, housed within the U.S. Centers for Disease Control and Prevention (CDC), tracks the number of adults in the United States who have health insurance. According to this agency, the uninsured rates for Americans in 2018 are as follows: 5.1% of those under the age of 18, 12.4% of those ages 18-64, and 1.1% of those 65and older do not have health insurance (CDC website). Approximately 22.8% of Americans are under age 18, and 61.4% of Americans are aged 18-64. Given that the person is an uninsured American, what is the probability that the person is 65 or older (to 3 decimals)?
Friendly’s Department Store has been the target of many shoplifters during the past month, but owing to increased security precautions ,250 shoplifters have been caught. Each shoplifter has been caught. Each shoplifter’s sex is noted; also noticed is whether the perpetrator was a first time or repeat offender. The data are summarized in the table .
Sex first time offender Repeat offender
Male 60 70
Female 44 76
146
Assume that an apprehended shoplifter is chosen at random, find
The probability that the shoplifter is male
The probability that the shoplifter is a first time offender, given that the shoplifter is male
The probability that the shoplifter is female and, given that the shoplifter is a repeat offender
The probability that the shoplifter is female and, given that the shoplifter first time offender.
The…
In the Aloha state, you are very unlikely to be murdered! However, it is considerably more likely that your house might be burgled, your car might be stolen, or you might be punched in the nose. That said, Hawaii is still a great place for a vacation or, if you are very lucky, to live. The following numbers represent the crime rates per 100,000 population in Hawaii: murder, 1.6; rape, 21.4; robbery, 95.3; house burglary, 903.6; motor vehicle theft, 521.7; assault, 106.3.
(a) Display this information in a Pareto chart, showing the crime rate for each category.
(b) Could the information as reported be displayed as a circle graph? Explain. Hint: Other forms of crime, such as arson, are not included in the information. In addition, some crimes might occur together.
A. Yes, but the graph would take into account only multiple crimes and not these particular individual crimes.
B. Yes, the graph would be able to account for all information.
C. No, the graph would be unable to account…
Chapter 11 Solutions
Essentials of Statistics (6th Edition)
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