Essentials of Statistics, Books a la Carte Edition (6th Edition)
6th Edition
ISBN: 9780134687131
Author: Mario F. Triola
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 11.1, Problem 22BSC
Ben ford’s Law. According to Benford’s law, a variety of different data sets include numbers with leading (first) digits that follow the distribution shown in the table below. In Exercises 21-24, test for goodness-of-fit with the distribution described by Benford’s law.
22. Author’s Check Amounts Exercise 21 lists the observed frequencies of leading digits from amounts on checks from seven suspect companies. Here are the observed frequencies of the leading digits from the amounts on the most recent checks written by the author at the time this exercise was created: 83, 58, 27, 21, 21, 21, 6, 4, 9. (Those observed frequencies correspond to the leading digits of 1, 2, 3, 4, 5, 6, 7, 8, and 9, respectively.) Using a 0.01 significance level, test the claim that these leading digits are from a population of leading digits that conform to Benford’s law. Does the conclusion change if the significance level is 0.05?
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Throughout, A, B, (An, n≥ 1), and (Bn, n≥ 1) are subsets of 2.
1. Show that
AAB (ANB) U (BA) = (AUB) (AB),
Α' Δ Β = Α Δ Β,
{A₁ U A2} A {B₁ U B2) C (A1 A B₁}U{A2 A B2).
16. Show that, if X and Y are independent random variables, such that E|X|< ∞,
and B is an arbitrary Borel set, then
EXI{Y B} = EX P(YE B).
Proposition 1.1 Suppose that X1, X2,... are random variables. The following
quantities are random variables:
(a) max{X1, X2) and min(X1, X2);
(b) sup, Xn and inf, Xn;
(c) lim sup∞ X
and lim inf∞ Xn-
(d) If Xn(w) converges for (almost) every w as n→ ∞, then lim-
random variable.
→ Xn is a
Chapter 11 Solutions
Essentials of Statistics, Books a la Carte Edition (6th Edition)
Ch. 11.1 - Cybersecurity The table below lists leading digits...Ch. 11.1 - 2. Cybersecurity When using the data from Exercise...Ch. 11.1 - Cybersecurity The accompanying Statdisk results...Ch. 11.1 - Cybersecurity What do the results from the...Ch. 11.1 - In Exercises 520, conduct the hypothesis test and...Ch. 11.1 - In Exercises 520, conduct the hypothesis test and...Ch. 11.1 - In Exercises 520, conduct the hypothesis test and...Ch. 11.1 - In Exercises 520, conduct the hypothesis test and...Ch. 11.1 - In Exercises 520, conduct the hypothesis test and...Ch. 11.1 - In Exercises 520, conduct the hypothesis test and...
Ch. 11.1 - In Exercises 520, conduct the hypothesis test and...Ch. 11.1 - In Exercises 520, conduct the hypothesis test and...Ch. 11.1 - In Exercises 520, conduct the hypothesis test and...Ch. 11.1 - In Exercises 520, conduct the hypothesis test and...Ch. 11.1 - In Exercises 520, conduct the hypothesis test and...Ch. 11.1 - In Exercises 520, conduct the hypothesis test and...Ch. 11.1 - Ben fords Law. According to Benfords law, a...Ch. 11.1 - Ben fords Law. According to Benfords law, a...Ch. 11.1 - Ben fords Law. According to Benfords law, a...Ch. 11.1 - Ben fords Law. According to Benfords law, a...Ch. 11.1 - Assumed mid-point x=fxn=39825180=221.25...Ch. 11.2 - Handedness and Cell Phone Use The accompanying...Ch. 11.2 - Ear Preference for Cell Phone Use 2. Hypotheses...Ch. 11.2 - Hypothesis Test The accompanying TI-83/84 Plus...Ch. 11.2 - Right-Tailed, Left-Tailed, Two-Tailed Is the...Ch. 11.2 - Prob. 5BSCCh. 11.2 - In Exercises 5-18, test the given claim. 6. Splint...Ch. 11.2 - In Exercises 5-18, test the given claim. 7....Ch. 11.2 - Prob. 8BSCCh. 11.2 - In Exercises 5-18, test the given claim. 9. Four...Ch. 11.2 - In Exercises 5-18, test the given claim. 10....Ch. 11.2 - In Exercises 5-18, test the given claim. 11....Ch. 11.2 - In Exercises 5-18, test the given claim. 12. Nurse...Ch. 11.2 - Soccer Strategy In soccer, serious fouls in the...Ch. 11.2 - In Exercises 5-18, lest the given claim. 14. Is...Ch. 11.2 - In Exercises 518, test the given claim. 15....Ch. 11.2 - In Exercises 5-18, test the given claim. 16....Ch. 11.2 - Prob. 17BSCCh. 11.2 - In Exercises 5-18, test the given claim. 18....Ch. 11.2 - In Exercises 5-18, lest the given claim. 19. Car...Ch. 11.2 - Is the Home Field Advantage Independent of the...Ch. 11.2 - Equivalent Tests A X2 test involving a 2 2 table...Ch. 11.2 - Using Yatess Correction for Continuity The...Ch. 11.3 - In Exercises 1-4, use the following listed arrival...Ch. 11.3 - In Exercises 1-4, use the following listed arrival...Ch. 11.3 - In Exercises 1-4, use the following listed arrival...Ch. 11.3 - In Exercises 1-4, use the following listed arrival...Ch. 11.3 - In Exercises 5-16, use analysis of variance for...Ch. 11.3 - In Exercises 5-16, use analysis of variance for...Ch. 11.3 - In Exercises 5-16, use analysis of variance for...Ch. 11.3 - In Exercises 5-16, use analysis of variance for...Ch. 11.3 - In Exercises 5-16, use analysis of variance for...Ch. 11.3 - Prob. 10BSCCh. 11.3 - Triathlon Times Jeff Parent is a statistics...Ch. 11.3 - Arsenic in Rice Listed below are amounts of...Ch. 11.3 - Prob. 13BSCCh. 11.3 - Speed Dating Listed below are attribute ratings of...Ch. 11.3 - Tukey Test A display of the Bonferroni test...Ch. 11.3 - Two-Way ANOVA The pulse rates in Table 12-3 from...Ch. 11 - Exercises 1-5 refer to the sample data in the...Ch. 11 - Exercises 15 refer to the sample data in the...Ch. 11 - Exercises 15 refer to the sample data in the...Ch. 11 - Prob. 4CQQCh. 11 - Exercises 15 refer to the sample data in the...Ch. 11 - Questions 610 refer to the sample data in the...Ch. 11 - Questions 610 refer to the sample data in the...Ch. 11 - Questions 6-10 refer to the sample data in the...Ch. 11 - Questions 6-10 refer to the sample data in the...Ch. 11 - Motor Vehicle Fatalities The table below lists...Ch. 11 - Tooth Fillings The table below shows results from...Ch. 11 - American Idol Contestants on the TV show American...Ch. 11 - Clinical Trial of Lipitor Lipitor is the trade...Ch. 11 - Weather-Related Deaths For a recent year, the...Ch. 11 - Weather-Related Deaths Review Exercise 5 involved...Ch. 11 - Chocolate and Happiness In a survey sponsored by...Ch. 11 - Chocolate and Happiness Use the results from part...Ch. 11 - Chocolate and Happiness Use the results from part...Ch. 11 - One Big Bill or Many Smaller Bills In a study of...Ch. 11 - 6. Probability Refer to the results from the 150...Ch. 11 - Car Repair Costs Listed below are repair costs (in...Ch. 11 - Forward Grip Reach and Ergonomics When designing...Ch. 11 - Use Statdisk, Minitab, Excel, StatCrunch, a...Ch. 11 - FROM DATA TO DECISION Critical Thinking: Was...Ch. 11 - Cola Weights Data Set 26 Cola Weights and Volumes...Ch. 11 - Speed Dating Data Set 18 Speed Dating in Appendix...Ch. 11 - Author Readability Pages were randomly selected by...
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
- Exercise 4.2 Prove that, if A and B are independent, then so are A and B, Ac and B, and A and B.arrow_forward8. Show that, if {Xn, n ≥ 1) are independent random variables, then sup X A) < ∞ for some A.arrow_forward8- 6. Show that, for any random variable, X, and a > 0, 8 心 P(xarrow_forward15. This problem extends Problem 20.6. Let X, Y be random variables with finite mean. Show that 00 (P(X ≤ x ≤ Y) - P(X ≤ x ≤ X))dx = E Y — E X.arrow_forward(b) Define a simple random variable. Provide an example.arrow_forward17. (a) Define the distribution of a random variable X. (b) Define the distribution function of a random variable X. (c) State the properties of a distribution function. (d) Explain the difference between the distribution and the distribution function of X.arrow_forward16. (a) Show that IA(w) is a random variable if and only if A E Farrow_forward15. Let 2 {1, 2,..., 6} and Fo({1, 2, 3, 4), (3, 4, 5, 6}). (a) Is the function X (w) = 21(3, 4) (w)+711.2,5,6) (w) a random variable? Explain. (b) Provide a function from 2 to R that is not a random variable with respect to (N, F). (c) Write the distribution of X. (d) Write and plot the distribution function of X.arrow_forward20. Define the o-field R2. Explain its relation to the o-field R.arrow_forward7. Show that An → A as n→∞ I{An} - → I{A} as n→ ∞.arrow_forward7. (a) Show that if A,, is an increasing sequence of measurable sets with limit A = Un An, then P(A) is an increasing sequence converging to P(A). (b) Repeat the same for a decreasing sequence. (c) Show that the following inequalities hold: P (lim inf An) lim inf P(A) ≤ lim sup P(A) ≤ P(lim sup A). (d) Using the above inequalities, show that if A, A, then P(A) + P(A).arrow_forward19. (a) Define the joint distribution and joint distribution function of a bivariate ran- dom variable. (b) Define its marginal distributions and marginal distribution functions. (c) Explain how to compute the marginal distribution functions from the joint distribution function.arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
Recommended textbooks for you
Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill
Holt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGAL
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