Calculate the 95% confidence interval for a sample of N = 28 with a mean = 15.86 and a population standard deviation (σ) = 10.00.
A) 95% CI = 15.86 ± 3.12
B) 95% CI = 15.86 ± 3.70
C) 95% CI = 15.86 ± 4.88
D) 95% CI = 15.86 ± 3.85

Question

Calculate the 95% confidence interval for a sample of N = 28 with a mean  = 15.86 and a population standard deviation (σ) = 10.00.
A) 95% CI = 15.86 ± 3.12 
B) 95% CI = 15.86 ± 3.70 
C) 95% CI = 15.86 ± 4.88 
D) 95% CI = 15.86 ± 3.85

Quizplus · Accepted Answer

The formula for the 95% confidence interval is:

CI = X ± (Z*σ/√N)

Where X is the sample mean, Z is the z-score for the desired confidence level (1.96 for 95%), σ is the population standard deviation, and N is the sample size.

Plugging in the values given:

CI = 15.86 ± (1.96*10/√28)
CI = 15.86 ± 3.70

Therefore, the best choice is B.

Calculate the 95% Confidence Interval for a Sample of N