The average heart rate for Indians is 72 beats per minute. To lower their heart rate, a group of 25 people participated in an aerobics exercise programme. The group was tested after six months to see if the group had significantly slowed their heart rate. The average heart rate for the group was 69 beats/minute with a standard deviation of 6.5. Was the aerobics program effective in lowering heart rate? (Given $α = 0.05$)
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → Yes, the program was effective; the reduction in heart rate is statistically significant.
Given $μ_0 = 72$ beasts/minute, $n = 25, \bar x = 69$ beats/minute and $S = 6.5$
Let the hypothesis be given as
Null hypothesis $H_0: μ≤72$
Alternative hypothesis $H_a: μ>72$.
So, the test statistics, $t =\frac{\bar x - μ_0}{\frac{S}{\sqrt{n}}}=\frac{69-72}{\frac{6.5}{\sqrt{25}}}=-\frac{3×5}{6.5}$
$⇒t=-2.3077$
$df = 25-1 = 24$, so $t_α= t_{0.05}$ at $df = 24$ is $t_{0.05} = 1.711$
$∵t< t_α$, so do not reject $H_0$.
Hence, the aerobics program was effective in lowering heart rate.