Suppose a random sample of 36 is selected from a population with a standard deviation of 12.If the sample mean is 98, the 99% confidence interval to estimate the population mean is ___.
A)94.08 to 101.92
B)92.85 to 103.15
C)97.35 to 98.65
D)93.34 to 102.66
E)90.20 to 105.00

Question

Quizplus · Accepted Answer

Use the formula: 
CI = x̄ ± z* (σ/√n)
where x̄ = 98, σ = 12, n = 36, and z* for a 99% confidence interval is 2.576. 
Plugging in the values, we get: 
CI = 98 ± 2.576 * (12/√36) 
CI = 98 ± 6.512 
CI = (98 - 6.512, 98 + 6.512) 
CI = (92.85, 103.15) 
Therefore, the 99% confidence interval to estimate the population mean is (92.85, 103.15), which is closest to option B.

Suppose a Random Sample of 36 Is Selected from a Population