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.

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