Statistics (13th Edition)
13th Edition
ISBN: 9780134080215
Author: James T. McClave, Terry T Sincich
Publisher: PEARSON
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Chapter 2.7, Problem 132UP
To determine
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Questions
An insurance company's cumulative incurred claims for the last 5 accident years are given
in the following table:
Development Year
Accident Year 0
2018
1 2 3 4
245 267 274 289 292
2019
255 276 288 294
2020
265 283 292
2021
263 278
2022
271
It can be assumed that claims are fully run off after 4 years. The premiums received for
each year are:
Accident Year Premium
2018
306
2019
312
2020
318
2021
326
2022
330
You do not need to make any allowance for inflation.
1. (a) Calculate the reserve at the end of 2022 using the basic chain ladder method.
(b) Calculate the reserve at the end of 2022 using the Bornhuetter-Ferguson method.
2. Comment on the differences in the reserves produced by the methods in Part 1.
To help consumers in purchasing a laptop computer, Consumer Reports calculates an overall test score for each computer tested based upon rating factors such as ergonomics, portability, performance, display, and battery life. Higher overall scores indicate better test results. The following data show the average retail price and the overall score for ten 13-inch models (Consumer Reports website, October 25, 2012).
Brand & Model
Price ($)
Overall Score
Samsung Ultrabook NP900X3C-A01US
1250
83
Apple MacBook Air MC965LL/A
1300
83
Apple MacBook Air MD231LL/A
1200
82
HP ENVY 13-2050nr Spectre XT
950
79
Sony VAIO SVS13112FXB
800
77
Acer Aspire S5-391-9880 Ultrabook
1200
74
Apple MacBook Pro MD101LL/A
1200
74
Apple MacBook Pro MD313LL/A
1000
73
Dell Inspiron I13Z-6591SLV
700
67
Samsung NP535U3C-A01US
600
63
a. Select a scatter diagram with price as the independent variable.
b. What does the scatter diagram developed in part (a) indicate about the relationship…
To the Internal Revenue Service, the reasonableness of total itemized deductions depends on the taxpayer’s adjusted gross income. Large deductions, which include charity and medical deductions, are more reasonable for taxpayers with large adjusted gross incomes. If a taxpayer claims larger than average itemized deductions for a given level of income, the chances of an IRS audit are increased. Data (in thousands of dollars) on adjusted gross income and the average or reasonable amount of itemized deductions follow.
Adjusted Gross Income ($1000s)
Reasonable Amount ofItemized Deductions ($1000s)
22
9.6
27
9.6
32
10.1
48
11.1
65
13.5
85
17.7
120
25.5
Compute b1 and b0 (to 4 decimals).b1 b0 Complete the estimated regression equation (to 2 decimals). = + x
Predict a reasonable level of total itemized deductions for a taxpayer with an adjusted gross income of $52.5 thousand (to 2 decimals). thousand dollarsWhat is the value, in dollars, of…
Chapter 2 Solutions
Statistics (13th Edition)
Ch. 2.1 - Explain the difference between class frequency,...Ch. 2.1 - Explain the difference between a bar graph and a...Ch. 2.1 - Explain the difference between a bar graph and a...Ch. 2.1 - Complete the following table:
Ch. 2.1 - 2.2 A qualitative variable with three classes (X,...Ch. 2.1 - Study of importance of libraries. In The Canadian...Ch. 2.1 - 2.5 Do social robots walk or roll? A social (or...Ch. 2.1 - Paying for music downloads. If you use the...Ch. 2.1 -
Cheek teeth of extinct primates. The...Ch. 2.1 - Humane education and classroom pets. In grade...
Ch. 2.1 -
Estimating the rhino population. The...Ch. 2.1 - STEM experiences for girls. The National Science...Ch. 2.1 - 2.7 Microsoft program security issues. To help its...Ch. 2.1 - Genealogy research. The Journal of Family History...Ch. 2.1 - Characteristics of ice melt ponds. The National...Ch. 2.1 - Railway track allocation. One of the problems...Ch. 2.1 - Satellites in orbit. According to the Union of...Ch. 2.1 - Curbing street gang gun violence. Operation...Ch. 2.1 - Interactions in a children’s museum. The nature of...Ch. 2.1 - 2.16 Motivation and right-oriented bias....Ch. 2.1 - Do you believe in the Bible? Each year the...Ch. 2.1 - Museum management. What criteria do museums use to...Ch. 2.1 - 2.17 Groundwater contamination in wells. In New...Ch. 2.1 - Extinct New Zealand birds. Refer to the...Ch. 2.2 - Explain the difference between a dot plot and a...Ch. 2.2 - Explain the difference between a bar graph and a...Ch. 2.2 - Explain the difference between the stem and the...Ch. 2.2 - In a histogram, what are the class intervals?
Ch. 2.2 - How many classes are recommended in a histogram of...Ch. 2.2 - 2.21 Minitab was used to generate the following...Ch. 2.2 - 2.20 Consider the stem-and-leaf display shown...Ch. 2.2 - 2.18 Graph the relative frequency histogram for...Ch. 2.2 - 2.19 Refer to Exercise 2.18. Calculate the number...Ch. 2.2 - Irrelevant speech effects. In a psychological...Ch. 2.2 - Stability of compounds in new drugs. Testing the...Ch. 2.2 - 2.23 Corporate sustainability of CPA firms. Refer...Ch. 2.2 - Shaft graves in ancient Greece. Archeologists have...Ch. 2.2 - Cheek teeth of extinct primates. Refer to the...Ch. 2.2 - Music performance anxiety. The nature of...Ch. 2.2 - Is honey a cough remedy? Does a teaspoon of honey...Ch. 2.2 - Sanitation inspection of cruise ships. To minimize...Ch. 2.2 - Crab spiders hiding on flowers. Crab spiders use...Ch. 2.2 - Sound waves from a basketball. An experiment was...Ch. 2.2 - Research on eating disorders. Data from a...Ch. 2.2 - Research on brain specimens. The postmortem...Ch. 2.2 - State SAT scores. Educators are constantly...Ch. 2.2 - 2.33 Phishing attacks to e-mail accounts. Phishing...Ch. 2.2 - Mineral flotation in water study. A high...Ch. 2.3 - Give three different measures of central...Ch. 2.3 - Explain the difference between a measure of...Ch. 2.3 - What is the symbol used to represent the sample...Ch. 2.3 - Explain the concept of a skewed distribution.
Ch. 2.3 - What two factors affect the accuracy of the sample...Ch. 2.3 - 2.41 Describe how the mean compares to the median...Ch. 2.3 - 2.35 Calculate the mean and median of the...Ch. 2.3 - 2.39 Calculate the mode, mean, and median of the...Ch. 2.3 - 2.36 Calculate the mean for samples where
n = 10,...Ch. 2.3 - Construct one data set consisting of five...Ch. 2.3 - 2.40 Calculate the mean, median, and mode for each...Ch. 2.3 - Use the applet entitled Mean versus Median to find...Ch. 2.3 - Use the applet Mean versus Median to illustrate...Ch. 2.3 - Use the applet Mean versus Median to study the...Ch. 2.3 - Prob. 60ACBCh. 2.3 - Characteristics of a rock fall. In Environmental...Ch. 2.3 - Music performance anxiety. Refer to the British...Ch. 2.3 - Corporate sustainability of CPA firms. Refer to...Ch. 2.3 - 2.49 Is honey a cough remedy? Refer to the...Ch. 2.3 - Check teeth of extinct primates. Refer to the...Ch. 2.3 - 2.52 Ranking driving performance of professional...Ch. 2.3 - 2.51 Symmetric or skewed? Would you expect the...Ch. 2.3 - Mongolian desert ants. The Journal of Biogeography...Ch. 2.3 - Permeability of sandstone during weathering....Ch. 2.3 - Mineral flotation in water study. Refer to the...Ch. 2.3 - Contact lenses for myopia. Myopia (i.e.,...Ch. 2.3 - Active nuclear power plants. The U.S. Energy...Ch. 2.4 - What is the range of data set?
Ch. 2.4 - Prob. 74UPCh. 2.4 - Prob. 75UPCh. 2.4 - Prob. 76UPCh. 2.4 - Prob. 77UPCh. 2.4 - 2.58 Calculate the variance and standard deviation...Ch. 2.4 - Prob. 79LMCh. 2.4 - Prob. 80LMCh. 2.4 - 2.62 Using only integers between 0 and 10,...Ch. 2.4 - Prob. 82LMCh. 2.4 - 2.63 Consider the following sample of five...Ch. 2.4 - Prob. 84LMCh. 2.4 - Use the applet entitled Standard Deviation to find...Ch. 2.4 - Use the applet Standard Deviation to study the...Ch. 2.4 - Use the applet Standard Deviation to study the...Ch. 2.4 - Shell lengths of sea turtles. Aquatic Biology...Ch. 2.4 - Shaft graves in ancient Greece. Refer to the...Ch. 2.4 - Music performance anxiety. Refer to the British...Ch. 2.4 - Characteristics of a rockfall. Refer to the...Ch. 2.4 - 2.68 Is honey a cough remedy? Refer to the...Ch. 2.4 - 2.65 Permeability of sandstone during weathering....Ch. 2.4 - Check teeth of extinct primates. Refer to the...Ch. 2.4 - 2.69 Active nuclear power plants. Refer to...Ch. 2.5 - To what kind of data sets can Chebyshev’s rule be...Ch. 2.5 - Prob. 94UPCh. 2.5 - Prob. 95UPCh. 2.5 - 2.72 For any set of data, what can be said about...Ch. 2.5 - 2.73 For a set of data with a mound-shaped...Ch. 2.5 - 2.74 The following is a sample of 25...Ch. 2.5 - 2.75 Given a data set with a largest value of 760...Ch. 2.5 - 2.78 Do social robots walk or roll? Refer to the...Ch. 2.5 - Sanitation inspection of cruise ships. Refer to...Ch. 2.5 - 2.80 Motivation of drug dealers. Consider a study...Ch. 2.5 - Dentists’ use of anesthetics. A study published in...Ch. 2.5 - Irrelevant speech effects. Refer to the Acoustical...Ch. 2.5 - Corporate sustainability of CPA firms. Refer to...Ch. 2.5 - Characteristics of antiwar demonstrators. The...Ch. 2.5 - Hand washing versus hand rubbing. As an...Ch. 2.5 - Velocity of Winchester bullets. The American...Ch. 2.5 - 2.77 Permeability of sandstone during weathering....Ch. 2.5 - 2.85 Shopping vehicle and judgment. While shopping...Ch. 2.5 - Animal-assisted therapy for heart patients. A...Ch. 2.5 - 2.87 Land purchase decision. A buyer for a lumber...Ch. 2.6 - For a quantitative data set
What is the 50th...Ch. 2.6 - 2.91 Give the percentage of measurements in a data...Ch. 2.6 - Prob. 116UPCh. 2.6 - 2.90 Compute the z-score corresponding to each of...Ch. 2.6 - Prob. 118LMCh. 2.6 - 2.94 Suppose that 40 and 90 are two elements of a...Ch. 2.6 - Math scores of twelfth graders. According to the...Ch. 2.6 - Drivers stopped by police. According to the Bureau...Ch. 2.6 - Stability of compounds in new drugs. Refer to the...Ch. 2.6 - Sanitation inspection of cruise ships. Refer to...Ch. 2.6 - Motivation of drug dealers. Refer to the Applied...Ch. 2.6 - 2.99 Lead in drinking water. The U.S....Ch. 2.6 - 2.96 Voltage sags and swells. Refer to the...Ch. 2.6 - 2.102 Blue- vs. red-colored exam study. In a study...Ch. 2.6 - 2.103 Ranking PhD programs in economics. Thousands...Ch. 2.6 - 2.105 Ranking PhD programs in economics (cont’d)....Ch. 2.6 - 2.104 Using z-scores for grades. At one...Ch. 2.7 - What is the interquartile range?
Ch. 2.7 - What are the hinges of a box plot?
Ch. 2.7 - With mound-shaped data, what proportion of the...Ch. 2.7 - Define an outlier.
Ch. 2.7 - 2.107 Suppose a data set consisting of exam scores...Ch. 2.7 - 2.108 Consider the horizontal box plot shown...Ch. 2.7 - 2.106 A sample data set has a mean of 57 and a...Ch. 2.7 - Consider the following sample data set. Construct...Ch. 2.7 - Consider the following sample data set.
Construct...Ch. 2.7 - Use the applet Standard Deviation to determine...Ch. 2.7 - Blond hair types in the Southwest Pacific. A...Ch. 2.7 - Dentists’ use of anesthetics. Refer to the Current...Ch. 2.7 - Research on brain specimens. Refer to the Brain...Ch. 2.7 - Prob. 144ACBCh. 2.7 - Prob. 145ACBCh. 2.7 - 2.112 Treating psoriasis with the “Doctorfish of...Ch. 2.7 - Sanitation Inspection of cruise ships. Refer to...Ch. 2.7 - Prob. 148ACICh. 2.7 - Prob. 149ACICh. 2.7 - Is honey a cough remedy? Refer to the Archives of...Ch. 2.7 - 2.119 Permeability of sandstone during weathering....Ch. 2.7 - Library book checkouts. A city librarian claims...Ch. 2.7 - Untutored second language acquisition. A student...Ch. 2.8 - Define a bivariate relationship.
Ch. 2.8 - Prob. 155UPCh. 2.8 - Prob. 156UPCh. 2.8 - Prob. 157LMCh. 2.8 - Prob. 158LMCh. 2.8 - Prob. 159ACBCh. 2.8 - Prob. 160ACBCh. 2.8 - Prob. 161ACBCh. 2.8 - Feeding behavior of fish. The feeding behavior of...Ch. 2.8 - New method for blood typing. In Analytical...Ch. 2.8 - Prob. 164ACICh. 2.8 - Plants that grow on Swiss cliffs. A rare plant...Ch. 2.8 - Prob. 166ACICh. 2.8 - Prob. 168ACACh. 2.8 - Ranking driving performance of professional...Ch. 2.9 - Museum management. Refer to the Museum Management...Ch. 2.9 - Trend in Iraq War casualties. While the United...Ch. 2.9 - 2.138 BP oil leak. In the summer of 2010, an...Ch. 2.9 - Irrelevant speech effects. Refer to the Acoustical...Ch. 2 - Prob. 174UPCh. 2 - 2.140 Discuss the conditions under which the...Ch. 2 - Prob. 176UPCh. 2 - Prob. 177UPCh. 2 - Prob. 178UPCh. 2 - Prob. 179LMCh. 2 - Prob. 180LMCh. 2 - Prob. 181LMCh. 2 - Prob. 182LMCh. 2 - Prob. 183LMCh. 2 - For each of the data sets in parts a–d, compute ,...Ch. 2 - Prob. 185LMCh. 2 - Prob. 186ACBCh. 2 - Prob. 187ACBCh. 2 - Reading Japanese books. Refer to Exercise 2.187....Ch. 2 - Prob. 189ACBCh. 2 - Crash tests on new cars. Each year, the National...Ch. 2 - Crash tests on new cars. Refer to Exercise 2.190...Ch. 2 - Estimating the age of glacial drifts. Tills are...Ch. 2 - Training zoo animals. “The Training Game” is an...Ch. 2 - Groundwater contamination in wells. Refer to the...Ch. 2 - Sociology fieldwork methods. University of New...Ch. 2 - Radioactive lichen. Lichen has a high absorbance...Ch. 2 - 2.88 Improving SAT scores. The National Education...Ch. 2 - Ammonia in car exhaust. Three-way catalytic...Ch. 2 - College protests of labor exploitation. The United...Ch. 2 - Speed of light front galaxies. Astronomers...Ch. 2 - Whistling dolphins. Marine scientists who study...Ch. 2 - Sentence complexity study. A study published in...Ch. 2 - Prob. 203ACICh. 2 - Archaeologists’ study of ring diagrams....Ch. 2 - Oil spill impact on seabirds. The Journal of...Ch. 2 - Benford’s Law of Numbers. According to Benford’s...Ch. 2 - Speed of light from galaxies. Refer to The...Ch. 2 - Standardized test “average.” U.S. News & World...Ch. 2 - Zinc phosphide in pest control. A chemical company...Ch. 2 - Grades in statistics. The final grades given by...Ch. 2 - Salaries of professional athletes. The salaries of...Ch. 2 - 2.170 No Child Left Behind Act. According to the...Ch. 2 - The Hite Report. Researcher Shere Hite shocked...
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