The following random sample from a population whose values were normally distributed was collected. 10
12
18
16

The 80% confidence interval for μ is
A) 12.054 to 15.946.
B) 10.108 to 17.892.
C) 10.321 to 17.679.
D) 11.009 to 16.991.

Question

The following random sample from a population whose values were normally distributed was collected. 10
12
18
16
​
The 80% confidence interval for μ is
A) 12.054 to 15.946.
B) 10.108 to 17.892.
C) 10.321 to 17.679.
D) 11.009 to 16.991.

Quizplus · Accepted Answer

The sample mean is 14 and the sample standard deviation is approximately 3.37. Using a t-distribution with 3 degrees of freedom (n-1=4-1=3) for an 80% confidence level, the critical t-value is approximately 1.638. The margin of error is calculated as t-value times the standard error (s/√n), resulting in the interval 11.009 to 16.991.

The Following Random Sample from a Population Whose Values Were