Question

andom 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: 68, 73, 71, 72, 64, 70, 68

Population 2: 74, 82, 81, 72, 76, 75, 75, 72

Is there evidence, at an α=0.05 level of significance, to conclude that there those who exercise regularly have lower resting heart rates? (Use the conservative method for computing degrees of freedom). Carry out an appropriate hypothesis test, filling in the information requested.

A. The value of the standardized test statistic:

B. The p-value is

C. Your decision for the hypothesis test:

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

Answer 1

= 69.43, s1 = 3.047, n1 = 7

= 75.75, s2 = 3.77, n2 = 8

H₀:

H₁:

A) The test statistic t = ()/sqrt(s1^2/n1 + s2^2/n2)

                                  = (69.43 - 75.75)/sqrt((3.047)^2/7 + (3.77)^2/8)

                                  = -3.59

B) DF = (s1^2/n1 + s2^2/n2)^2/((s1^2/n1)^2/(n1 - 1) + (s2^2/n2)^2/(n2 - 1))

         = ((3.047)^2/7 + (3.77)^2/8)^2/(((3.047)^2/7)^2/6 + ((3.77)^2/8)^2/7)

         = 13

P-value = P(T < -3.59)

             = 0.0016

C) Since the P-value is less than the significance level(0.0016 < 0.05), so we should reject the null hypothesis.

Option - D) Reject H₀.