CONFIDENCE INTERVAL FOR mu1

CONFIDENCE INTERVAL FOR m₁ - m₂

INDEPENDENT SAMPLES

It is desired to compare the mean breaking strength of corrugated fiberboard made by two different manufactures. The breaking strengths of a random sample of 10 fiberboards made by Manufacturer 1 are obtained, and the breaking strengths of a second random sample of 10 fiberboards made by Manufacturer 2 are obtained. These data, measured in pounds per square inch are shown below.

Estimate the difference in the mean breaking strength of the two brands of fiberboard using 95% confidence.

SOLUTION

Since there are two different, unrelated, random samples, the samples are independent, and the parameter of interest is m ₁ – m _{2 ,} the difference in the mean breaking strengths of fiberboard made by Manufacturer 1 vs. those made by Manufacturer 2.

Calculations from StatCrunch: -10.86 to -1.34

Interpretation: I am 95% confident that the mean breaking strength of all fiberboard made by the first manufacturer is between 10.86 and 1.34 pounds per square inch less than the mean breaking strength of all fiberboard made by the second manufacturer.

COMMENTS ABOUT THE SOLUTION

This procedure is valid when both populations of breaking strengths are normally distributed, both samples are random, and the two samples are independent from each other.

The procedure in this problem is also valid when large samples are randomly selected from any population, regardless of its original distribution. Generally speaking samples of 30 or more are considered large.

The usual structure for presenting the solution to a confidence interval was followed. All confidence interval solutions should follow this structure.

When interpreting a confidence interval that compares two population means always be sure to phrase the interpretation in terms of how much larger (or smaller) the first mean is as compared to the second mean.

The complete StatCrunch analyses are below.

95% confidence interval results:
μ₁ : mean of Manufacturer 1
μ₂ : mean of Manufacturer 2
μ₁ - μ₂ : mean difference
(without pooled variances)

Difference

Sample Mean

Std. Err.

DF

L. Limit

U. Limit

m1 - m2

-6.1

2.2521594

16.738905

-10.857293

-1.3427067

Difference	Sample Mean	Std. Err.	DF	L. Limit	U. Limit
m1 - m2	-6.1	2.2521594	16.738905	-10.857293	-1.3427067