Understanding Basic Statistics
7th Edition
ISBN: 9781305254060
Author: Charles Henry Brase, Corrinne Pellillo Brase
Publisher: Cengage Learning
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Chapter 8.2, Problem 19P
19
Critical Thinking: Boxplots and Confidence Intervals The distribution of heights of 18-year-old men in the United States is approximately normal. with
| VARIABLE | N | MEAN | STDEV | SEMEAN | 95.0 | % CI |
| Sample 1 | 20 | 68.050 | 2.901 | 0.649 | 69.407) | |
| Sample a | 20 | 67.956 | 3.137 | 0.702 | (66.490 | 69.426 |
| Sample 3 | 20 | 67.976 | 2.639 | 0.590 | (66.741 , | 69.211) |
| Sample 4 | 20 | 66.908 | 2.440 | 0.546 | (65.766 , | 68.050) |
(a) Examine the figure (parts (a) to (d)). How do the boxplots for the four samples differ? Why should you expect the boxplots to differ ?
(b) Examine the 95% confidence intervals for the four sample shown in the printout. Do the intervals differ in length? Do the intervals all contain the expected population mean of tot inches? If we draw more samples, do you expect all of the resulting 95% confidence intervals to contain µ = 68 ? Why or why not?
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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 8 Solutions
Understanding Basic Statistics
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