Introductory Statistics
3rd Edition
ISBN: 9780135188927
Author: Gould, Robert, Ryan, Colleen N. (colleen Nooter)
Publisher: Pearson,
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Chapter 9, Problem 6SE
Smartphones According to a 2017 report by ComScore .com, the
a. Suppose 150 American adults are randomly surveyed and asked how long they spend on their smartphones daily. The mean of the sample is recorded. Then we repeat this process, taking 1000 surveys of 150 American adults and recording the sample means. What will be the shape of the distribution of these sample means?
b. Refer to part (a). What will be the mean and the standard deviation of the distribution of these sample means?
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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 9 Solutions
Introductory Statistics
Ch. 9 - Ages A study of all the students at a small...Ch. 9 - Units A survey of 100 random full-time students at...Ch. 9 - Exam Scores The distribution of the scores on a...Ch. 9 - Exam Scores The distribution of the scores on a...Ch. 9 - Showers According to home-water-works.org, the...Ch. 9 - Smartphones According to a 2017 report by ComScore...Ch. 9 - Retirement Income Several times during the year,...Ch. 9 - Time Employed A human resources manager for a...Ch. 9 - Driving (Example 1) Drivers in Wyoming drive more...Ch. 9 - Driving Drivers in Alaska drive fewer miles yearly...
Ch. 9 - Babies Weights (Example 2) Some sources report...Ch. 9 - Babies’ Weights, Again Some sources report that...Ch. 9 - (Example 3) Income in Maryland According to a 2018...Ch. 9 - Income in Kansas According to a 2018 Money...Ch. 9 - CLT Shapes (Example 4) One of the histograms is a...Ch. 9 - Used Van Costs One histogram shows the...Ch. 9 - (Example 5) Age of Used Vans The mean age of all...Ch. 9 - Student Ages The mean age of all 2550 students at...Ch. 9 - Prob. 19SECh. 9 - Prob. 20SECh. 9 - Prob. 21SECh. 9 - Prob. 22SECh. 9 - Private University Tuition (Example 7) A random...Ch. 9 - Random Numbers If you take samples of 40 lines...Ch. 9 - t* (Example 8) A researcher collects one sample of...Ch. 9 - t* A researcher collects a sample of 25...Ch. 9 - Heights of 12th Graders (Example 9) A random...Ch. 9 - Drinks A fast-food chain sells drinks that it...Ch. 9 - Men’s Pulse Rates (Example 10) A random sample of...Ch. 9 - Travel Time to School A random sample of 50...Ch. 9 - RBIs (Example 11) A random sample of 25 baseball...Ch. 9 - RBIs Again In exercise 9.31, two intervals were...Ch. 9 - Confidence Interval Changes State whether each of...Ch. 9 - Confidence Interval Changes State whether each of...Ch. 9 - Potatoes The weights of four randomly and...Ch. 9 - Tomatoes The weights of four randomly and...Ch. 9 - Human Body Temperatures (Example 12) A random...Ch. 9 - Reaction Distance Data on the disk and website...Ch. 9 - Potatoes Use the data from exercise 9.35. a. If...Ch. 9 - Tomatoes Use the data from exercise 9.36. a. Using...Ch. 9 - Cholesterol In the U.S. Department of Health has...Ch. 9 - BMI A body mass index (BMI) of more than 25 is...Ch. 9 - Male Height In the United States, the population...Ch. 9 - Female Height In the United States, the population...Ch. 9 - Deflated Footballs? Patriots In the 2015 AFC...Ch. 9 - Deflated Footballs? Colts In the 2015 AFC...Ch. 9 - Movie Ticket Prices According to Deadline.com, the...Ch. 9 - Broadway Ticket Prices According to Statista.com,...Ch. 9 - Atkins Diet Difference Ten people went on an...Ch. 9 - Pulse Difference The following numbers are the...Ch. 9 - Student Ages Suppose that 200 statistics students...Ch. 9 - Presidents’ Ages at Inauguration A 95 confidence...Ch. 9 - Independent or Paired (Example 13) State whether...Ch. 9 - Independent or Paired State whether each situation...Ch. 9 - Televisions: CI (Example 14) Minitab output is...Ch. 9 - Pulse and Gender: CI Using data from NHANES, we...Ch. 9 - Televisions (Example 15) The table shows the...Ch. 9 - Pulse Rates Using data from NHANES, we looked at...Ch. 9 - Triglycerides Triglycerides are a form of fat...Ch. 9 - Systolic Blood Pressures When you have your blood...Ch. 9 - Triglycerides, Again Report and interpret the 95...Ch. 9 - Blood Pressures, Again Report and interpret the 95...Ch. 9 - Baseball Salaries A random sample of 40...Ch. 9 - College Athletes’ Weights A random sample of male...Ch. 9 - Baseball Salaries In exercise 9.63 you could not...Ch. 9 - College Athletes’ Weights In exercise 9.64, you...Ch. 9 - Textbook Prices, UCSB vs. CSUN (Example 16) The...Ch. 9 - Textbook Prices. OC vs. CSUN The prices of a...Ch. 9 - Females’ Pulse Rates before and after a Fright...Ch. 9 - Males’ Pulse Rates before and after a Fright...Ch. 9 - Organic Food A student compared organic food...Ch. 9 - Body Temperature The body temperatures of 65 men...Ch. 9 - Ales vs. IPAs Data were collected on calorie...Ch. 9 - Surfers Surfers and statistics students Rex...Ch. 9 - Self-Reported Heights of Men (Example 18) A random...Ch. 9 - Eating Out Jacqueline Loya, a statistics student,...Ch. 9 - Prob. 77SECh. 9 - Self-Driving Cars A survey of asked respondents...Ch. 9 - Women’s Heights Assume women’s heights are...Ch. 9 - Showers According to home-water-works.org, the...Ch. 9 - Choose a test for each situation: one-sample...Ch. 9 - Choose a t-test for each situation: one-sample...Ch. 9 - Cones: 3 Tests A McDonald’s fact sheet says its...Ch. 9 - Prob. 84CRECh. 9 - Brain Size Brain size for 20 random women and 20...Ch. 9 - Reducing Pollution A random sample of 12th-grade...Ch. 9 - Heart Rate before and after Coffee Elena Lucin, a...Ch. 9 - Exam Grades The final exam grades for a sample of...Ch. 9 - Hours of Television Viewing The number of hours...Ch. 9 - Reaction Distances Reaction distances in...Ch. 9 - Ales vs. Lagers Data were collected on calorie...Ch. 9 - Weights of Hockey and Baseball Players Data were...Ch. 9 - Grocery Delivery The table shows the prices for...Ch. 9 - Parents The following table shows the heights (in...Ch. 9 - Why Is n1 in the Sample Standard Deviation? Why do...Ch. 9 - Prob. 96CRECh. 9 - Construct two sets of body temperatures (in...Ch. 9 - Construct heights for 3 or more sets of twins (6...
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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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