Constructing 96% Confidence Interval Estimate
What is the formula to construct a 96% confidence interval estimate of the average difference in fill weights for the 2 production lines?
Given the summary measures from the samples, how do we interpret the practical meaning of the resulting confidence interval in plain English?
Answer:
The confidence interval is (-0.70, 0.98). This indicates that with 96% confidence, it can be defined that the value of the sample difference will be between this interval.
Explanation:
The given data is as follows:
μ1 =24.89
n1=22
σ1^2 =0.0081
μ2=25.03
n2=25
σ2^2 =0.0196
With this data, the mean difference formula is given as:
CI @ 96% is given by:
(x1, x2)=(μ2-μ1) ± z_{α}√(σ1^2/n1 + σ2^2/n2)
The values are as given above. z_{α} is 2.05 for the 96% confidence interval.
(x1, x2)=(μ2-μ1) ± z_{α}√(σ1^2/n1 + σ2^2/n2)
(x1, x2)=(25.03-24.89) ± 2.05√(0.0081/22 + 0.0196/25)
(x1, x2)=(0.14) ± 0.84
(x1, x2)=(-0.70, 0.98)
So, the confidence interval is (-0.70, 0.98). This means that with 96% confidence, we can state that the value of the sample difference will fall within this interval.