Essentials of Statistics (6th Edition)
6th Edition
ISBN: 9780134687155
Author: Triola
Publisher: PEARSON
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Chapter 11.1, Problem 13BSC
In Exercises 5–20, conduct the hypothesis test and provide the test statistic and the P-value and/or critical value, and state the conclusion.
13. Kentucky Derby The table below lists the frequency of wins for different post positions through the 141st running of the Kentucky Derby horse race. A post position of 1 is closest to the inside rail, so the horse in that position has the shortest distance to run. (Because the number of horses varies from year to year, only the first 10 post positions are included.) Use a 0.05 significance level to test the claim that the likelihood of winning is the same for the different post positions. Based on the result, should bettors consider the post position of a horse racing in the Kentucky Derby?
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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 (6th Edition)
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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...
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- 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
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