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:  69,69,70,65,69,70,72

Population 2:  74,71,70,69,68,69,75,68

Is there evidence, at an α=0.01 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:

(b) The rejection region for the standardized test statistic:

(c) Your decision for the hypothesis test:
A. Reject H1.
B. Do Not Reject H1.
C. Do Not Reject H0.
D. Reject H0.

Answer 1

 = 69.143, s1 = 2.1156, n1 = 7

 = 70.5, s2 = 2.6726, n2 = 8

H₀:

H₁:

The pooled variance (s_p²) = ((n1 - 1)s1^2 + (n2 - 1)s2^2)/(n1 + n2 - 2) = (6 * (2.1156)^2 + 7 * (2.6726)^2)/(7 + 8 - 2) = 5.912

a) The test statistic t = ()/sqrt(s_p²/n1 + s_p²/n2)

= (69.143 - 70.5)/sqrt(5.912/7 + 5.912/8) = -1.08

b) df = 7 + 8 - 2 = 13

At alpha = 0.01, the critical value is t_{0.01, 13} = -2.650

Reject H₀, if the < -2.650

C) Since the test statistic value is not less than the critical value (-1.08 > -2.650), so we should not reject the null hypothesis.

Option - C) Do not reject H0.