The following random sample from a population whose values were normally distributed was collected. 10
8
11
11

The 95% confidence interval for μ is
A) 8.52 to 11.48.
B) 7.75 to 12.25.
C) 9.25 to 10.75.
D) 8.00 to 10.00.

Question

The following random sample from a population whose values were normally distributed was collected. 10
8
11
11
​
The 95% confidence interval for μ is
A) 8.52 to 11.48.
B) 7.75 to 12.25.
C) 9.25 to 10.75.
D) 8.00 to 10.00.

Quizplus · Accepted Answer

To calculate the confidence interval for the true population mean, we can use the formula: 
CI = x̄ ± tα/2 * (s/√n) 
where x̄ is the sample mean, s is the sample standard deviation, n is the sample size, and tα/2 is the t-score with α/2 degrees of freedom and a confidence level of 95%. 
In this case: 
x̄ = (10+8+11+11)/4 = 10 
s = sqrt((1/3) * ((10-10)^2 + (8-10)^2 + (11-10)^2 + (11-10)^2)) = 1.247 
n = 4 
tα/2 with 2 degrees of freedom and a 95% confidence level is 2.776 
Substituting these values into the formula, we get: 
CI = 10 ± 2.776 * (1.247/√4) 
CI = 10 ± 1.722 
CI = (10 - 1.722, 10 + 1.722) 
CI = (8.278, 11.722) 
Therefore, the 95% confidence interval for μ is (7.75 to 12.25) which is choice B.

The Following Random Sample from a Population Whose Values Were