Understanding Basic Statistics
8th Edition
ISBN: 9781337558075
Author: Charles Henry Brase, Corrinne Pellillo Brase
Publisher: Cengage Learning
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Chapter 1.2, Problem 19P
Sampling Methods: Benefits Package An important part of employee compensation isa benefits package, which might include health insurance, life insurance. child care, vacation days, retirement plan, parental leave, bonuses, etc. Suppose you want to conduct a survey of benefits packages available in private businesses in Hawaii. You want a
(a) Assign each business in the Island Business Directory a number, and then use a random-number table to select the businesses to be included in the sample.
(b) Use postal ZIP Codes to divide the state into regions. Pick a random sample of 10 ZIP Code areas, and then include all the businesses in each selected ZIP Code area.
(c) Send a team of five research assistants to Bishop Street in downtown Honolulu. Let each assistant select a block or building and interview an employee from each business found. Bach researcher can have the rest of the day off after getting responses from 20 different businesses.
(d) Use the Island Business Directory. Number all the businesses. Select a starting place at random, and then use every 50th business listed until you have 100 businesses.
(e) Group the businesses according to type: medical, shipping, retail, manufacturing, financial, construction, restaurant, hotel, tourism, other. Then select a random sample of 10 businesses from each business type.
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2. Which of the following statements are (not) true?
lim sup{An U Bn}
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lim sup{A, B}
818
lim inf{An U Bn}
818
818
lim inf{A, B}
An
An A, Bn-
A, BnB
→B
=
=
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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→∞.
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).
Chapter 1 Solutions
Understanding Basic Statistics
Ch. 1.1 - Statistical Literacy In a statistical study, what...Ch. 1.1 - Statistical Literacy Are data at the nominal level...Ch. 1.1 - Statistical Literacy What is the difference...Ch. 1.1 - Statistical Literacy For a set population, does a...Ch. 1.1 - Critical Thinking Numbers are often assigned to...Ch. 1.1 - Interpretation Lucy conducted a survey asking some...Ch. 1.1 - Marketing: Fast Food A national survey asked 1261...Ch. 1.1 - Advertising: Auto Mileage What is the average...Ch. 1.1 - Ecology: Wetlands Government agencies carefully...Ch. 1.1 - Archaeology: Ireland The archaeological site of...
Ch. 1.1 - Student Life: Levels of Measurement Categorize...Ch. 1.1 - Business: Levels of Measurement Categorize these...Ch. 1.1 - Fishing: Levels of Measurement Categorize these...Ch. 1.1 - Education: Teacher Evaluation If you were going to...Ch. 1.1 - Critical Thinking You are interested in the...Ch. 1.2 - Statistical Literacy Explain the difference...Ch. 1.2 - Statistical Literacy Explain the difference...Ch. 1.2 - Statistical Literacy Marcie conducted a study of...Ch. 1.2 - Statistical Literacy A random sample of students...Ch. 1.2 - Interpretation In a random sample of 50 students...Ch. 1.2 - Interpretation A campus performance series...Ch. 1.2 - Critical Thinking Greg took a random sample of...Ch. 1.2 - Critical Thinking Consider the students in your...Ch. 1.2 - Critical Thinking Suppose you are assigned the...Ch. 1.2 - Critical Thinking In each of the following...Ch. 1.2 - Sampling: Random Use a random-number table to...Ch. 1.2 - Sampling: Random Use a random-number table to...Ch. 1.2 - Sampling: Random Use a random-number table to...Ch. 1.2 - Prob. 14PCh. 1.2 - Computer Simulation: Roll of a Die A die is a cube...Ch. 1.2 - Prob. 16PCh. 1.2 - Education: Test Construction Professor Gill is...Ch. 1.2 - Education: Test Construction Professor Gill uses...Ch. 1.2 - Sampling Methods: Benefits Package An important...Ch. 1.2 - Sampling Methods: Health Care Modern Managed...Ch. 1.3 - Statistical Literacy A study of college graduates...Ch. 1.3 - Statistical Literacy Consider a completely...Ch. 1.3 - Critical Thinking A brief survey regarding...Ch. 1.3 - Critical Thinking A randomized block design was...Ch. 1.3 - Interpretation Zane is examining two studies...Ch. 1.3 - Interpretation Suppose you are looking at the 2006...Ch. 1.3 - Ecology: Gathering Data Which technique for...Ch. 1.3 - General: Gathering Data Which technique for...Ch. 1.3 - General: Completely Randomized Experiment How...Ch. 1.3 - Survey: Manipulation The NewYork Times did a...Ch. 1.3 - Critical Thinking An agricultural study is...Ch. 1 - Terminology If a numerical measure describes an...Ch. 1 - Terminology If a variable describes an individual...Ch. 1 - Prob. 3CRCh. 1 - Terminology If it makes sense to say that one data...Ch. 1 - Terminology Consider a sample of size n. If every...Ch. 1 - Terminology If a treatment is applied to subjects...Ch. 1 - Critical Thinking Sudoku is a puzzle consisting of...Ch. 1 - Critical Thinking Alisha wants to Jo a statistical...Ch. 1 - Statistical Literacy You are conducting a study of...Ch. 1 - Radio Talk Show: Sample Bias A radio talk show...Ch. 1 - Prob. 11CRCh. 1 - General: Type of Sampling Categorize the type of...Ch. 1 - General: Gathering Data Which technique fur...Ch. 1 - General: Experiment How would you use a completely...Ch. 1 - Student Life: Data Collection Project Make a...Ch. 1 - Form Problem: Fireflies Suppose you air conducting...Ch. 1 - Use a random-number table or random-number...Ch. 1 - Use a random-number table or random-number...Ch. 1 - What does it mean to say that we are going to use...Ch. 1 - In your own words, explain the differences among...Ch. 1 - Simulate the results of tossing a fair die 18...Ch. 1 - Prob. 2UTA
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- 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_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_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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