Calculate the 99% confidence interval for a sample of N = 30 with a mean = 1376.41 and standard error of the mean = 30.73.
A) 99% CI = 1376.41 ± 62.84
B) 99% CI = 1376.41 ± 52.15
C) 99% CI = 1376.41 ± 84.81
D) 99% CI = 1376.41 ± 33.48

Question

Calculate the 99% confidence interval for a sample of N = 30 with a mean  = 1376.41 and standard error of the mean  = 30.73.
A) 99% CI = 1376.41 ± 62.84 
B) 99% CI = 1376.41 ± 52.15 
C) 99% CI = 1376.41 ± 84.81 
D) 99% CI = 1376.41 ± 33.48

Quizplus · Accepted Answer

The 99% confidence interval can be calculated using the formula: 
CI = X̄ ± t(α/2, n-1) * SEM
where X̄ is the sample mean, SEM is the standard error of the mean, n is the sample size, and t(α/2, n-1) is the t-score for the desired level of confidence and degrees of freedom.

For a 99% confidence interval with 30 degrees of freedom, we use t(α/2, n-1) = 2.750.

Substituting the given values into the formula, we get: 
CI = 1376.41 ± 2.750 * 30.73
CI = 1376.41 ± 84.81

Therefore, the correct choice is C.

Calculate the 99% Confidence Interval for a Sample of N