Confidence Interval Changes State whether each of the following changes would make a confidence interval wider or narrower. (Assume that nothing else changes.) a. Changing from a 95 % level of confidence to a 90 % level of confidence b. Changing from a sample size of 30 to a sample size of 20 c. Changing from a standard deviation of 3 inches to a standard deviation of 2.5 inches
Confidence Interval Changes State whether each of the following changes would make a confidence interval wider or narrower. (Assume that nothing else changes.) a. Changing from a 95 % level of confidence to a 90 % level of confidence b. Changing from a sample size of 30 to a sample size of 20 c. Changing from a standard deviation of 3 inches to a standard deviation of 2.5 inches
Solution Summary: The author explains how the width of the interval decreases with the decrease in the confidence level, and the margin of error increases when the sample size increases.
Confidence Interval Changes State whether each of the following changes would make a confidence interval wider or narrower. (Assume that nothing else changes.)
a. Changing from a
95
%
level of confidence to a
90
%
level of confidence
b. Changing from a sample size of 30 to a sample size of 20
c. Changing from a standard deviation of 3 inches to a standard deviation of
2.5
inches
Definition Definition Number of subjects or observations included in a study. A large sample size typically provides more reliable results and better representation of the population. As sample size and width of confidence interval are inversely related, if the sample size is increased, the width of the confidence interval decreases.
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
Precalculus: Mathematics for Calculus (Standalone Book)
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