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: 72, 71, 65, 65, 72, 73, 70

Population 2: 72, 72, 75, 70, 73, 69, 77, 77

Is there evidence, at an α=0.06 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 H1.

C. Reject H1.

D. Do Not Reject H0.

Answer 1

(A)

H0: Null Hypothesis:    ( Those who exercise regularly do not have lower resting heart rates )

HA: Alternative Hypothesis:    ( Those who exercise regularly have lower resting heart rates ) (Claim)

From the given data, the following statistics are calculated:

n1 = 7

1 = 69.7143

s1 = 3.3523

n2 = 8

2 = 73.1250

s2 = 2.9970

Pooled Standard Diviation is given by:

Test Statisticis given by:

So,

The value of the standardized test statistic: = - 2.0816

(B)

= 0.06

df = 7 +8 - 2 = 13

From Table, critical value of t = - 1.664

The rejection region for the standardized test statistic: ( - , - 1.664)

(C)

By Technology,

p - value = 0.0289

(D)

Correct option:

A. Reject H0.