Pearson eText for Essentials of Statistics -- Instant Access (Pearson+)
6th Edition
ISBN: 9780137517374
Author: Mario Triola
Publisher: PEARSON+
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Chapter 9.3, Problem 15BSC
In Exercises 5–16, use the listed paired sample data, and assume that the samples are simple random samples and that the differences have a distribution that is approximately normal.
15. Hypnotism for Reducing Pain A study was conducted to investigate the effectiveness of hypnotism in reducing pain. Results for randomly selected subjects are given in the accompanying table (based on “An Analysis of Factors That Contribute to the Efficacy of Hypnotic Analgesia.” by Price and Barber, Journal of Abnormal Psychology, Vol. 96, No. 1). The values are before and after hypnosis; the measurements are in centimeters on a pain scale. Higher values correspond to greater levels of pain. Construct a 95% confidence interval for the
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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
Pearson eText for Essentials of Statistics -- Instant Access (Pearson+)
Ch. 9.1 - Verifying Requirements In the largest clinical...Ch. 9.1 - Verifying Requirements In the largest clinical...Ch. 9.1 - Hypotheses and Conclusions Refer to the hypothesis...Ch. 9.1 - Using Confidence Intervals a. Assume that we want...Ch. 9.1 - Interpreting Displays. In Exercises 5 and 6, use...Ch. 9.1 - Treating Carpal Tunnel Syndrome Carpal tunnel...Ch. 9.1 - Testing Claims About Proportions. In Exercises...Ch. 9.1 - Accuracy of Fast Food Drive-Through Orders In a...Ch. 9.1 - Testing Claims About Proportions. In Exercises...Ch. 9.1 - Testing Claims About Proportions. In Exercises...
Ch. 9.1 - Testing Claims About Proportions. In Exercises...Ch. 9.1 - Testing Claims About Proportions. In Exercises...Ch. 9.1 - Testing Claims About Proportions. In Exercises...Ch. 9.1 - Testing Claims About Proportions. In Exercises...Ch. 9.1 - Testing Claims About Proportions. In Exercises...Ch. 9.1 - Prob. 16BSCCh. 9.1 - Testing Claims About Proportions. In Exercises...Ch. 9.1 - Testing Claims About Proportions. In Exercises...Ch. 9.1 - Testing Claims About Proportions. In Exercises...Ch. 9.1 - Testing Claims About Proportions. In Exercises...Ch. 9.1 - Testing Claims About Proportions. In Exercises...Ch. 9.1 - Testing Claims About Proportions. In Exercises...Ch. 9.1 - Prob. 23BBCh. 9.1 - Yawning and Fishers Exact Test In one segment of...Ch. 9.1 - Overlap of Confidence Intervals In the article On...Ch. 9.1 - Equivalence of Hypothesis Test and Confidence...Ch. 9.2 - Independent and Dependent Samples Which of the...Ch. 9.2 - Confidence Interval for Hemoglobin Large samples...Ch. 9.2 - Hypothesis Tests and Confidence Intervals for...Ch. 9.2 - Degrees of Freedom For Example 1 on page 431, we...Ch. 9.2 - In Exercises 520, assume that the two samples are...Ch. 9.2 - In Exercises 520, assume that the two samples are...Ch. 9.2 - In Exercises 520, assume that the two samples are...Ch. 9.2 - In Exercises 520, assume that the two samples are...Ch. 9.2 - In Exercises 520, assume that the two samples are...Ch. 9.2 - In Exercises 520, assume that the two samples are...Ch. 9.2 - In Exercises 520, assume that the two samples are...Ch. 9.2 - In Exercises 520, assume that the two samples are...Ch. 9.2 - In Exercises 520, assume that the two samples are...Ch. 9.2 - In Exercises 520, assume that the two samples are...Ch. 9.2 - In Exercises 520, assume that the two samples are...Ch. 9.2 - In Exercises 520, assume that the two samples are...Ch. 9.2 - In Exercises 520, assume that the two samples are...Ch. 9.2 - In Exercises 520, assume that the two samples are...Ch. 9.2 - In Exercises 520, assume that the two samples are...Ch. 9.2 - In Exercises 520, assume that the two samples are...Ch. 9.2 - Pooling Repeat Exercise 12 IQ and Lead by assuming...Ch. 9.2 - Degrees of Freedom In Exercise 20 Blanking Out on...Ch. 9.2 - No Variation in a Sample An experiment was...Ch. 9.3 - True? For the methods of this section, which of...Ch. 9.3 - Notation Listed below are body temperatures from...Ch. 9.3 - Units of Measure If the values listed in Exercise...Ch. 9.3 - Degrees of Freedom If we use the sample data in...Ch. 9.3 - In Exercises 516, use the listed paired sample...Ch. 9.3 - In Exercises 516, use the listed paired sample...Ch. 9.3 - In Exercises 516, use the listed paired sample...Ch. 9.3 - In Exercises 516, use the listed paired sample...Ch. 9.3 - In Exercises 516, use the listed paired sample...Ch. 9.3 - In Exercises 516, use the listed paired sample...Ch. 9.3 - Prob. 11BSCCh. 9.3 - Prob. 12BSCCh. 9.3 - In Exercises 516, use the listed paired sample...Ch. 9.3 - In Exercises 516, use the listed paired sample...Ch. 9.3 - In Exercises 516, use the listed paired sample...Ch. 9.3 - In Exercises 516, use the listed paired sample...Ch. 9 - In Exercises 15, use the following survey results:...Ch. 9 - In Exercises 1-5, use the following survey...Ch. 9 - In Exercises 1-5, use the following survey...Ch. 9 - In Exercises 1-5, use the following survey...Ch. 9 - In Exercises 7-5, use the following survey...Ch. 9 - True? Determine whether the following statement is...Ch. 9 - True? When we collect random samples to test the...Ch. 9 - Dependent or Independent? Listed below are...Ch. 9 - Hypotheses Identify the null and alternative...Ch. 9 - Test Statistics Identify the test statistic that...Ch. 9 - Denomination Effect In the article The...Ch. 9 - Denomination Effect Construct the confidence...Ch. 9 - Heights Listed below are heights (cm) randomly...Ch. 9 - Heights Use a 0.01 significance level with the...Ch. 9 - Before /After Treatment Results Captopril is a...Ch. 9 - Eyewitness Accuracy of Police Does stress affect...Ch. 9 - Are Flights Cheaper When Scheduled Earlier? Listed...Ch. 9 - Family Heights. In Exercises 15, use the following...Ch. 9 - Scatterplot Construct a scatterplot of the...Ch. 9 - Family Heights. In Exercises 1-5, use the...Ch. 9 - Family Heights. In Exercises 1-5, use the...Ch. 9 - Assessing Normality Interpret the normal quantile...Ch. 9 - Braking Reaction Times: Histogram Listed below are...Ch. 9 - Braking Reaction Times: Normal? The accompanying...Ch. 9 - Braking Reaction Times: Boxplots Use the same data...Ch. 9 - In Exercises 5-20, assume that the two samples are...Ch. 9 - Braking Reaction Times: Confidence Intervals a....Ch. 9 - FROM DATA TO DECISION Critical Thinking: Did the...Ch. 9 - Critical Thinking: Did the NFL Rule Change Have...Ch. 9 - Critical Thinking: Did the NFL Rule Change Have...
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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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