Question

A sample of 25 Brand W 40-gallon water heaters was found to have a mean life of 12 years with a standard deviation of s = 2 years. Construct a 95% confidence interval to estimate the population mean life of these water heaters, to 4 decimal places. (Note that σ is unknown)

Answer 1

Solution:
Given in the question
Number of sample (n) = 25
Sample mean (Xbar) = 12
Sample standard deviation (S) = 2
We need to calculate 95% confidence interval to estimate the population mean life of these water heaters, Here we will use t test as population standard deviation σ is unknown and sample size n is less than 30 so 95% confidence interval can be calculated as
Xbar +/- talpha/2 * S/sqrt(n)
Here confidence level = 0.95
level of significance = 0.05
alpha/2 = 0.025
degree of freedom = n-1 = 25-1 = 24
from t table we found talpha/2 at df=24 and alpha/2 = 0.025 is 2.064
Xbar +/- talpha/2 * S/sqrt(n)
12 +/- 2.064*2/sqrt(25)
12 +/- 0.8256
So 95% confidence interval is 11.1744 to 12.8256
we are 95% confident that mean life of these water heaters is between 11.1744 years to 12.8256 years