Question

3. For a group of 22 college football players, the mean heart rate after a morning workout session was 86 beats per minute, and the standard deviation was 5. Find and interpret the 90% confidence interval of the true mean for all college football players after a workout session.

Answer 1

Given:

Sample size = n = 22

Standard deviation = s = 5

Sample mean = = 86

Significance level = =1- 0.90 = 0.10

Degree of freedom = df = n - 1 = 22 - 1 = 21   

At 90% confidence level, the critical value of t is

t/2, df = t0.10/2, 21 = 1.7207

90% conference interval is

= 86 1.7207 * 5/√22

= 86 1.8343

= (84.1657, 87.8343)

Therefore 90% confidence interval is (84.1657, 87.8343)

Interpretation : We are 90% confident that the true mean for all college football players after a workout session is between 84.1657 and 87.8343