Statistics: The Art and Science of Learning from Data (4th Edition)
4th Edition
ISBN: 9780321997838
Author: Alan Agresti, Christine A. Franklin, Bernhard Klingenberg
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 11, Problem 65CP
Clarity of diamonds Does the clarity of a diamond depend on its cut? Exercise 3.4 showed data, reproduced below, on the clarity (rated as internally flawless, IF. very very slightly included, VVS, very slightly included, VS, slightly included, SI and included. I) for the two lowest ratings for cut, which are “good” and “fair.”
- a. Verify, using software, that X2 = 0.267 for this table. The (raw) data are available on the book’s website as Diamonds.csv.
- b. Can you use the chi-squared distribution to find a P-value? Why or why not?
- c. Of 10,000 random permutations. 9,908 resulted in an X2 value as large or larger than the one observed. Find the (approximate) permutation P-value and interpret.
- d. Use the Permutation Test of Independence web app accessible from the book’s website to enter the
contingency table and replicate the results from part c.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Determine which of the four levels of measurement is most appropriate for the data below
The following times to failure (TTFs) of several ball bearings were found
during a recent wearout test at the manufacturing facility. Conduct a
graphical Weibull analysis by hand of these failure times and estimate the
characteristic life and the shape factor. Include your completed Weibull plot
in your answer The times to failure are:
211 242 179 175 254 85 150 136 138 202
Ocean currents are important in studies of climate change, as well as ecology studies of dispersal of plankton. Drift bottles are used to study ocean currents in the Pacific near Hawaii, the Solomon Islands, New Guinea, and other islands. Let x represent the number of days to recovery of a drift bottle after release and y represent the distance from point of release to point of recovery in km/100. The following data are representative of one study using drift bottles to study ocean currents.
x days
76
79
36
95
207
y km/100
14.2
19.6
5.4
11.2
35.9
(a) Verify that
Σx = 493,
Σy = 86.3,
Σx2 = 65,187,
Σy2 = 2029.21,
Σxy = 11317.3,
and
r ≈ 0.93885.
Σx
Σy
Σx2
Σy2
Σxy
r
(b) Use a 1% level of significance to test the claim
ρ > 0.
(Use 2 decimal places.)
t
critical t
(c) Verify that
Se ≈ 4.6183,
a ≈ 0.5575,
and
b ≈ 0.1694.
Se
a
b
Find the predicted distance (km/100) when a drift bottle has been floating for 60 days. (Use 2…
Chapter 11 Solutions
Statistics: The Art and Science of Learning from Data (4th Edition)
Ch. 11.1 - Gender gap in politics? In the United States, is...Ch. 11.1 - Prob. 2PBCh. 11.1 - Williams College admission Data from 2013 posted...Ch. 11.1 - Prob. 4PBCh. 11.1 - Marital happiness and income In the GSS, subjects...Ch. 11.1 - What is independent of happiness? Which one of the...Ch. 11.1 - Sample evidence about independence Refer to the...Ch. 11.2 - Life after death and gender In the 2012 GSS, 605...Ch. 11.2 - Happiness and gender For the 2 3 table on gender...Ch. 11.2 - Prob. 10PB
Ch. 11.2 - Marital happiness and income In Exercise 11.5 when...Ch. 11.2 - First and second free throw independent? In pro...Ch. 11.2 - Cigarettes and marijuana The table on the...Ch. 11.2 - Prob. 14PBCh. 11.2 - Help the environment In 2010 the GSS asked whether...Ch. 11.2 - Prob. 16PBCh. 11.2 - Aspirin and heart attacks A Swedish study used...Ch. 11.2 - z test for heart attack study Refer to the...Ch. 11.2 - Severity of fever after flu shot The study...Ch. 11.2 - Prob. 20PBCh. 11.2 - Testing a genetic theory In an experiment on...Ch. 11.2 - Birthdays by quarters Based on a random sample of...Ch. 11.2 - Checking a roulette wheel Karl Pearson devised the...Ch. 11.3 - Democrat, race, and gender The two tables show...Ch. 11.3 - Death penalty associations Table 11.10, summarized...Ch. 11.3 - Smoking and alcohol The table refers to a survey...Ch. 11.3 - Sex of victim and offender For murders in the...Ch. 11.3 - Smelling and mortality A recent study (Pinto et...Ch. 11.3 - Vioxx In September 2004, the pharmaceutical...Ch. 11.3 - Egg and cell derived vaccine When comparing the...Ch. 11.3 - Risk of dying for teenagers According to...Ch. 11.3 - Marital happiness The table shows 2012 GSS data on...Ch. 11.3 - Party ID and gender The table shows the 2012 GSS...Ch. 11.3 - Chi-squared versus measuring association For the...Ch. 11.4 - Standardized residuals for happiness and income...Ch. 11.4 - Prob. 36PBCh. 11.4 - Prob. 37PBCh. 11.4 - Prob. 38PBCh. 11.4 - Prob. 39PBCh. 11.4 - Prob. 40PBCh. 11.5 - Keeping old dogs mentally sharp In an experiment...Ch. 11.5 - Prob. 43PBCh. 11.5 - Prob. 44PBCh. 11.5 - Prob. 46PBCh. 11 - Female for president? When recent General Social...Ch. 11 - Prob. 48CPCh. 11 - Down and chi-squared For the data in the previous...Ch. 11 - Prob. 50CPCh. 11 - Prob. 51CPCh. 11 - Prob. 52CPCh. 11 - Prob. 53CPCh. 11 - Prob. 54CPCh. 11 - Prob. 55CPCh. 11 - Prob. 56CPCh. 11 - Seat belt helps? The table refers to passengers in...Ch. 11 - Prob. 58CPCh. 11 - Prob. 59CPCh. 11 - Prob. 60CPCh. 11 - Prob. 61CPCh. 11 - Prob. 62CPCh. 11 - Prob. 63CPCh. 11 - Prob. 64CPCh. 11 - Clarity of diamonds Does the clarity of a diamond...Ch. 11 - Benfords Law When looking at a collection of...Ch. 11 - Prob. 67CPCh. 11 - Prob. 68CPCh. 11 - Prob. 70CPCh. 11 - Prob. 71CPCh. 11 - Prob. 72CPCh. 11 - Prob. 73CPCh. 11 - Prob. 74CPCh. 11 - Prob. 75CPCh. 11 - Prob. 76CPCh. 11 - Prob. 77CPCh. 11 - Prob. 78CPCh. 11 - Prob. 79CPCh. 11 - Statistical versus practical significance In any...Ch. 11 - Prob. 81CPCh. 11 - Multiple response variables Each subject in a...Ch. 11 - Standardized residuals for 2 2 tables The table...Ch. 11 - Prob. 84CPCh. 11 - Prob. 85CPCh. 11 - Prob. 86CPCh. 11 - Prob. 87CPCh. 11 - Prob. 88CPCh. 11 - Voting with 16 A recent survey of Austrian high...
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.Similar questions
- Find the mean hourly cost when the cell phone described above is used for 240 minutes.arrow_forward12:51 K A pediatrician wants to determine the relation that exists between a child's height, x, and head circumference, y. She randomly selects 11 children from her practice, measures their heights and head circumferences, and obtains the accompanying data. Complete parts (a) through (g) below. Click the icon to view the children's data. Data Table (a) Find the least-squares regression line treating height as the explanatory variable and head circumference as the response variable. y = x+ (Round the slope to three decimal places and round the constant to one decimal place as needed.) Height (inches), x Head Circumference (inches), y 27.5 17.4 24.5 17.0 25.75 17.0 26 17.5 24.25 16.8 27.75 17.5 26.25 17.2 17.4 17.2 17.4 17.4 27.25 26.5 26.5 27.75 Vol) 1 LTE2 = Print ا... ا... Done 45% Xarrow_forwardThe Quick Sell car dealership has been using 1-minute spot ads on a local TV station. The ads always occur during the evening hours and advertise the different models and price ranges of cars on the lot that week. During a 10-week period, the Quick Sell dealer kept a weekly record of the number x of TV ads versus the number y of cars sold. The results are given in Table below. . ( Show your work--No work no credit) x y 6 15 20 31 0 10 14 16 25 28 16 20 28 40 18 25 10 12 8 15 Draw a scatter diagram for the data ( You can copy and past this graph in your work area by using any technology). Do you see a linear relation? Compute the value of linear correlation coefficient "r". From the value of "r" can we decide the strength of the relation ( strong, moderate, or weak)? Find the equation of regression line, identify the slope and intercept. Also explain meaning of slope in the context of the problem. How many cars can the manager expect to sell if 12 ads per…arrow_forward
- Ocean currents are important in studies of climate change, as well as ecology studies of dispersal of plankton. Drift bottles are used to study ocean currents in the Pacific near Hawaii, the Solomon Islands, New Guinea, and other islands. Let x represent the number of days to recovery of a drift bottle after release and y represent the distance from point of release to point of recovery in km/100. The following data are representative of one study using drift bottles to study ocean currents. 203 x days y km/100 72 76 32 14.7 94 11.7 19.5 5.3 35.6 (a) Verify that Ex = 477, Ey = 86.8, Ex? = 62,029, Ey2 = 2028.68, Exy = 11036.6, and r= 0.93853. Ex Ey Ex? Ey2| Exy (b) Use a 1% level of significance to test the claim p> 0. (Use 2 decimal places.) critical t Conclusion Reject the null hypothesis, there is sufficient evidence that p > 0. Reject the null hypothesis, there is insufficient evidence that p > 0. O Fail to reject the null hypothesis, there is insufficient evidence that p > 0. O…arrow_forwardOcean currents are important in studies of climate change, as well as ecology studies of dispersal of plankton. Drift bottles are used to study ocean currents in the Pacific near Hawaii, the Solomon Islands, New Guinea, and other islands. Let x represent the number of days to recovery of a drift bottle after release and y represent the distance from point of release to point of recovery in km/100. The following data are representative of one study using drift bottles to study ocean currents. x days 74 77 34 96 208 y km/100 14.9 19.1 5.8 11.9 35.7 (a) Find Σx, Σy, Σx2, Σy2, Σxy, and r. (Round r to three decimal places.) Σx = Σy = Σx2 = Σy2 = Σxy = r = (b) Use a 1% level of significance to test the claim ρ > 0. (Round your answers to two decimal places.) t = critical t = Conclusion Reject the null hypothesis, there is sufficient evidence that ρ > 0.Reject the null hypothesis, there is insufficient evidence that ρ >…arrow_forwardOcean currents are important in studies of climate change, as well as ecology studies of dispersal of plankton. Drift bottles are used to study ocean currents in the Pacific near Hawaii, the Solomon Islands, New Guinea, and other islands. Let x represent the number of days to recovery of a drift bottle after release and y represent the distance from point of release to point of recovery in km/100. The following data are representative of one study using drift bottles to study ocean currents. x days 75 79 35 91 203 y km/100 14.2 19.1 5.8 11.2 35.4 (a) Verify that Σx = 483, Σy = 85.7, Σx2 = 62,581, Σy2 = 1978.69, Σxy = 10982.3, and r ≈ 0.94895. Σx Σy Σx2 Σy2 Σxy r (b) Use a 1% level of significance to test the claim ρ > 0. (Use 2 decimal places.) t critical t (c) Verify that Se ≈ 4.1118, a ≈ 0.7378, and b ≈ 0.1698. Se a barrow_forward
- Ocean currents are important in studies of climate change, as well as ecology studies of dispersal of plankton. Drift bottles are used to study ocean currents in the Pacific near Hawaii, the Solomon Islands, New Guinea, and other islands. Let x represent the number of days to recovery of a drift bottle after release and y represent the distance from point of release to point of recovery in km/100. The following data are representative of one study using drift bottles to study ocean currents. x days 75 79 35 91 203 y km/100 14.2 19.1 5.8 11.2 35.4 (d) Find the predicted distance (km/100) when a drift bottle has been floating for 80 days. (Use 2 decimal places.) km/100(e) Find a 90% confidence interval for your prediction of part (d). (Use 1 decimal place.) lower limit km/100 upper limit km/100 (f) Use a 1% level of significance to test the claim that β > 0. (Use 2 decimal places.) t critical t (g) Find a 95% confidence interval for β and interpret…arrow_forwardWhich of the following best describes the process of finding the interquartile range for a set of data? a.Find the difference between the maximum and the minimum. b.Subtract Q1 from Q3. c.Add the biggest and smallest numbers. d.Place the numbers in order from least to greatest and find the middle.arrow_forwardEyeglassomatic manufactures eyeglasses for different retailers. They test to see how many defective lenses they made the time period of January 1 to March 31. The table gives the defect and the number of defects. Do the data support the notion that each defect type occurs in the same proportion? Test at the 5% level. Number of Defective Lenses Defect type Number of defects Scratch 1866 Right shaped - small 1935 Flaked 1979 Wrong axis 1921 Chamfer wrong 1864 Crazing, cracks 1991 Wrong shape 2004 Wrong PD 1895 Spots and bubbles 1917 Wrong height 1885 Right shape - big 1875 Lost in lab 1886 Spots/bubble - intern 1935 State the hypotheses.H0: Each defect type in the same proportion.Ha: Each defect type in the same proportion. Calculate the χ2 test statistic. Round expected values to two decimal places. Round χ2 to three decimal places.χ2 = Calculate the p-value. Round to four decimal places.p-value = State your decision.Since p-value 0.05,…arrow_forward
- Find the new data point (x,y) in which x=2 from the data points (1.3) and (4.12)arrow_forwardIt has been determined that there is a significant relationship between the temperature (x) and the number of times that a cricket chirps in a minute (y). Below is a table of values: Number of Temperature chirps 69.7 882 93.3 1188 84.3 1104 76.3 864 88.6 1200 82.6 1032 71.6 960 79.6 900arrow_forwardMatch the value of the corelation to the data in the scatterplot. (a) (b) (c) Ar=-0.51 vScatterplot (a) vScatterplot (b) VScatterplot (c) vScatterplot (d) B.r= 0.89 C.r = 0.99 D.r= - 0.12arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
Big Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin Harcourt
Trigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage Learning
Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill
Holt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGAL
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage
Big Ideas Math A Bridge To Success Algebra 1: Stu...
Algebra
ISBN:9781680331141
Author:HOUGHTON MIFFLIN HARCOURT
Publisher:Houghton Mifflin Harcourt
Trigonometry (MindTap Course List)
Trigonometry
ISBN:9781337278461
Author:Ron Larson
Publisher:Cengage Learning
Glencoe Algebra 1, Student Edition, 9780079039897...
Algebra
ISBN:9780079039897
Author:Carter
Publisher:McGraw Hill
Holt Mcdougal Larson Pre-algebra: Student Edition...
Algebra
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
The Shape of Data: Distributions: Crash Course Statistics #7; Author: CrashCourse;https://www.youtube.com/watch?v=bPFNxD3Yg6U;License: Standard YouTube License, CC-BY
Shape, Center, and Spread - Module 20.2 (Part 1); Author: Mrmathblog;https://www.youtube.com/watch?v=COaid7O_Gag;License: Standard YouTube License, CC-BY
Shape, Center and Spread; Author: Emily Murdock;https://www.youtube.com/watch?v=_YyW0DSCzpM;License: Standard Youtube License