Given a sample mean of 27 and a sample standard deviation of 3.5 computed from a sample of size 36, find a 95% confidence interval on the population mean.
A) [25.8158, 28.1842]
B) [25.8170, 28.1830]
C) [26.0142, 27.9858]
D) [26.9930, 27.0070]

Question

Quizplus · Accepted Answer

We can use the formula: 
CI = X ± Z(α/2) * (σ/√n)
where X is the sample mean, Z(α/2) is the z-score at α/2 level of confidence (α = 1 - 0.95 = 0.05, so α/2 = 0.025), σ is the population standard deviation (unknown), and n is the sample size.

Substituting the values given:
CI = 27 ± 1.96 * (3.5 /√36)
CI = 27 ± 1.96 * (0.5833)
CI = [25.8158, 28.1842]

Therefore, the best choice is A.

Given a Sample Mean of 27 and a Sample Standard