Question

c. Confidence Interval given the sample standard deviation:

5. Confidence Interval, σ is not known or n<30.

For a group of 20 students taking a final exam, the mean heart rate was 96 beats per minute and the standard deviation was 5. Find the 95% confidence interval of the true mean.  

e) Find the critical value:

f) Find the margin of error: E =tα/2sn√

g) Find the confidence interval: CI = x−± E.

h) Write the conclusion.

Answer 1

Answer 5: Confidence Interval, σ is not known or n<30.

For a group of 20 students, the mean heart rate was 96 beats per minute and the standard deviation was 5.

Find the 95% confidence interval of the true mean.

Solution:

n = 20

Mean x̄ = 96

Standard deviation, s = 5

At 95% confidence interval, α = 0.05

e) Find the critical value:

df = n-1 = 20 - 1 = 19

t critical = t(α/2,df) = t(0.025,19)

t critical = 2.0930

f) Find the margin of error: E =tα/2sn√

margin of error, E = t critical * s/√n

E = 2.0930 * 5 / √19

E = 2.4008

g) Find the confidence interval: CI = x−± E.

the 95% confidence interval for mean:

CI = x̄ ± E

CI = 96 ± 2.4008

CI = (93.5992, 98.4008)

h) Write the conclusion.

Therefore, the 95% confidence interval for mean is between 93.5992 and 98.4008.

the 95% confidence interval of the true mean is

93.5992 < μ < 98.4008.