Introductory Statistics (2nd Edition)
2nd Edition
ISBN: 9780321978271
Author: Robert Gould, Colleen N. Ryan
Publisher: PEARSON
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Chapter 11, Problem 6SE
a.
To determine
Determine and compare the
c .
To determine
Determine the test statistic and compare all possible pairs of means.
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17. Suppose that X1, X2,..., Xn are random variables, such that E|xk| < ∞ for
all k, and set Yn = max1
6. Show that, for any random variable, X, and a > 0,
L
P(x < X ≤ x+a) dx = a.
2015
15. This problem extends Problem 20.6. Let X, Y be random variables with finite
mean. Show that
(P(X ≤ x ≤ Y) - P(Y < x ≤ X))dx = E Y — E X.
Chapter 11 Solutions
Introductory Statistics (2nd Edition)
Ch. 11 - Choosing a Test a. You wish to test whether an...Ch. 11 - Prob. 2SECh. 11 - Bonferroni Correction (Example 1) Suppose you have...Ch. 11 - Prob. 4SECh. 11 - Prob. 5SECh. 11 - Prob. 6SECh. 11 - Prob. 7SECh. 11 - Prob. 8SECh. 11 - Prob. 9SECh. 11 - Prob. 10SE
Ch. 11 - Gas Price Intervals Use the data from exercise...Ch. 11 - Gas Price Intervals Use the data from exercise...Ch. 11 - Work Hours and Education The table shows the...Ch. 11 - Prob. 14SECh. 11 - Comparing F -Values from Boxplots (Example 3)...Ch. 11 - Comparing F -Values from Boxplots Refer to the...Ch. 11 - Marital Status and Cholesterol (Example 4) Refer...Ch. 11 - Marital Status and Blood Pressure Test the...Ch. 11 - Schoolwork and Class (Example 5) A random survey...Ch. 11 - TV Hours A random survey was done at a small...Ch. 11 - Schoolwork and Class Use the information for...Ch. 11 - TV Hours Use the information for exercise 11.20....Ch. 11 - Schoolwork Again Go back to the information in...Ch. 11 - TV Hours Again Go back to the information in...Ch. 11 - Pulse Rates (Example 6) Pulse rates were taken for...Ch. 11 - UCLA Music Survey The figure shows side-by-side...Ch. 11 - Commute Times by Method A survey was given to...Ch. 11 - Prob. 30SECh. 11 - Prob. 31SECh. 11 - Study Hours by Major Three independent random...Ch. 11 - Salary by Type of College Information was gathered...Ch. 11 - Draft Lottery When the draft lottery for military...Ch. 11 - Reaction Times for Athletes A random sample of...Ch. 11 - Tomato Plants and Colored Light Jennifer Brogan, a...Ch. 11 - GPAs by Seating Choice A random sample of students...Ch. 11 - Reading Comprehension Sixty-six reading students...Ch. 11 - Hours of Steep and Health Status In a study done...Ch. 11 - Happiness and Age Category StatCrunch surveyed...Ch. 11 - Prob. 41SECh. 11 - House Prices Tukey HSD confidence intervals (with...Ch. 11 - GPA and Row (Example 8) A random sample of...Ch. 11 - Reading Scores by Teaching Method Refer to...Ch. 11 - Reaction Distances Use the data given in exercise...Ch. 11 - Study Hours Use the data given in exercise 11.32....Ch. 11 - Baseball Player Run-Times (Example 9) Determine...Ch. 11 - Tomatoes Use the data given in exercise 11.36....Ch. 11 - Concern over Nuclear Power Following the...Ch. 11 - Immigration Issue A survey was done by StatCrunch...Ch. 11 - Happiness and Age Consider the data from the...Ch. 11 - GPA and Row Number Suppose you collect data on...Ch. 11 - Contacting Mother Professors of ethics (Eth),...Ch. 11 - Ideal Percentage to Charity Professors of ethics...Ch. 11 - Actual Percentage to Charity Professors of ethics...Ch. 11 - Hours of Television by Age Group The StatCrunch...Ch. 11 - Triglycerides and Gender Using the NHANES data, we...Ch. 11 - Cholesterol and Gender Using NHANES data, we...
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- 2. Which of the following statements are (not) true? lim sup{An U Bn} 818 lim sup{A, B} 818 lim inf{An U Bn} 818 818 lim inf{A, B} An An A, Bn- A, BnB →B = = = lim sup A, U lim sup Bn; 818 818 lim sup A, lim sup Bn; 818 81U lim inf A, U lim inf Bn; 818 818 lim inf A, lim inf Bn; n→X 818 An U BRAUB as no; An OBRANB as n→∞.arrow_forwardThroughout, 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).arrow_forward16. 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).arrow_forward
- 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 aarrow_forwardExercise 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_forward
- 8- 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_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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