Question

Random samples of resting heart rates are taken from two groups. Population 1 exercises regularly, and Population 2 does not. The data from these two samples is given below:

Population 1: 71, 68, 67, 70, 70, 70, 67

Population 2: 69, 70, 73, 69, 76, 79, 75, 78

Is there evidence, at an α=0.02 level of significance, to conclude that there those who exercise regularly have lower resting heart rates? (Assume that the population variances are equal.) Carry out an appropriate hypothesis test, filling in the information requested.

A. The value of the standardized test statistic:

Note: For the next part, your answer should use interval notation. An answer of the form (−∞,a) is expressed (-infty, a), an answer of the form (b,∞) is expressed (b, infty), and an answer of the form (−∞,a)∪(b,∞) is expressed (-infty, a)U(b, infty).

B. The rejection region for the standardized test statistic:

C. The p-value is

D. Your decision for the hypothesis test:

A. Reject H0.
B. Do Not Reject H0
C. Do Not Reject H1.
D. Reject H1.

Answer 1

t-Test: Two-Sample Assuming Equal Variances
	Population1	Population2
Mean	69	73.625
Variance	2.666667	15.98214
Observations	7	8
Pooled Variance	9.836538
Hypothesized Mean Difference	0
df	13
t Stat	-2.84931
P(T<=t) one-tail	0.006838
t Critical one-tail	2.281604
P(T<=t) two-tail	0.013675
t Critical two-tail	2.650309

A. The value of the standardized test statistic:

=((69-73.625)-0)/sqrt(2.66/6+15.98/7)

=-2.8

The value of the standardized test statistic: =-2.8

B. The rejection region for the standardized test statistic:

we reject Ho if T-stat < -2.28

C. The p-value is

P(T<=-2.8493) one-tail =0.0068

D. Your decision for the hypothesis test:

A. Reject H0.

since p-value < 0.02