Calculate the lower and upper limits of the 95% confidence interval for a sample of N = 25 with a mean = 4.06 and standard error of the mean = .27.
A) (3.50, 4.62)
B) (3.60, 4.52)
C) (3.30, 4.82)
D) (1.73, 6.39)

Question

Calculate the lower and upper limits of the 95% confidence interval for a sample of N = 25 with a mean  = 4.06 and standard error of the mean  = .27.
A) (3.50, 4.62) 
B) (3.60, 4.52) 
C) (3.30, 4.82) 
D) (1.73, 6.39)

Quizplus · Accepted Answer

To calculate the confidence interval, we use the formula:

Confidence interval = X̄ ± (Z*SE)

where X̄ is the sample mean, SE is the standard error of the mean, and Z is the z-score corresponding to the desired level of confidence (in this case, 95%).

From the given information, X̄ = 4.06 and SE = 0.27. The z-score corresponding to the 95% confidence level is 1.96.

Substituting these values into the formula, we get:

Confidence interval = 4.06 ± (1.96*0.27)
Confidence interval = 4.06 ± 0.53

Therefore, the lower and upper limits of the 95% confidence interval are:

Lower limit = 4.06 - 0.53 = 3.53
Upper limit = 4.06 + 0.53 = 4.59

Rounding to two decimal places gives (3.50, 4.62), which corresponds to choice A.

Calculate the Lower and Upper Limits of the 95% Confidence