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: 65, 64, 69, 73, 67, 64, 70

Population 2: 74, 78, 75, 69, 69, 73, 79, 74

Is there evidence, at an α=0.05α=0.05 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 p-value is

D. Your decision for the hypothesis test:

A. Reject H1H1.
B. Do Not Reject H0H0.
C. Do Not Reject H1H1.
D. Reject H0H0.

Answer 1

To test,

Ho:1-2=0 v/s H1:1-2<0

# Minitab Output:

Two-Sample T-Test and CI: population 1, population 2

Two-sample T for population 1 vs population 2

N Mean StDev SE Mean
population 1 7 67.43 3.41 1.3
population 2 8 73.88 3.64 1.3

Difference = mu (population 1) - mu (population 2)
Estimate for difference: -6.44643
95% upper bound for difference: -3.20506
T-Test of difference = 0 (vs <): T-Value = -3.52 P-Value = 0.002 DF = 13
Both use Pooled StDev = 3.5365

From above output,

# Test statistic=-3.52

# P value=0.002

Where P value < 0.05 ( alpha level)

# Hence,we reject Ho.