Heart Rate before and after Coffee Elena Lucin, a statistics student, collected the data in the table showing heart rate (beats per minute) for a random sample of coffee drinkers before and 15 minutes after they drank coffee. Carry out a complete analysis, using the techniques you learned in this chapter. Use a 5 % significance level to test whether coffee increases heart rate. The same amount of caffeinated coffee was served to each person, and you may assume that conditions for a t -test hold.
Heart Rate before and after Coffee Elena Lucin, a statistics student, collected the data in the table showing heart rate (beats per minute) for a random sample of coffee drinkers before and 15 minutes after they drank coffee. Carry out a complete analysis, using the techniques you learned in this chapter. Use a 5 % significance level to test whether coffee increases heart rate. The same amount of caffeinated coffee was served to each person, and you may assume that conditions for a t -test hold.
Solution Summary: The author explains how to perform a paired test using the MINITAB software.
Heart Rate before and after Coffee Elena Lucin, a statistics student, collected the data in the table showing heart rate (beats per minute) for a random sample of coffee drinkers before and 15 minutes after they drank coffee. Carry out a complete analysis, using the techniques you learned in this chapter. Use a
5
%
significance level to test whether coffee increases heart rate. The same amount of caffeinated coffee was served to each person, and you may assume that conditions for a
t
-test
hold.
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
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