In: Statistics and Probability
A group of researchers was trying to evaluate the influence of exercise on humans pulse rate. Two measurements were made to understand the effect of exercise to pulse rates, one at the beginning (Baseline) and one at the end of 2 months of routine excersise
Baseline Pulses: 72 76 70 69 74
After Exercise: 68 73 66 65 70
Find the 95% confidence interval estimate for the average reduction in pulse rate. The differences in pulse rates before and after exercise are assumed normally distributed. And, at 5% level of significance, test to see if the difference in pulse rates before and after exercise is statistically significant.
= (4 + 3 + 4 + 4 + 4)/5 = 3.8
sd = sqrt(((4 - 3.8)^2 + (3 - 3.8)^2 + (4 - 3.8)^2 + (4 - 3.8)^2 + (4 - 3.8)^2)/4) = 0.4472
At 95% confidence interval the critical value is t* = 2.777
The 95% confidence interval is
+/- t* * sd/
= 3.8 +/- 2.777 * 0.4472/
= 3.8 +/- 0.555
= 3.245, 4.355
H0: = 0
H1: 0
The test statistic t = ( - D)/(sd/)
= (3.8 - 0)/(0.4472/)
= 19.00
At 0.05 significance level, the critical values are t* = +/- 2.777
Since the test statistic value is greater than the positive critical value(19 > 2.777), so we should reject the null hypothesis.
So there is sufficient evidence to conclude that there is a significant difference in pulse rates before and after exercise.