Math Problem Statement

A manufacturing company wants to compare the average production output of two of its plants. Plant X has a sample of 40 days with an average daily production of 150 units and a standard deviation of 15 units. Plant Y has a sample of 35 days with an average daily production of 145 units and a standard deviation of 12 units. Test at the 1% significance level whether there is a significant difference in the average daily production output between the two plants.

Solution

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Math Problem Analysis

Mathematical Concepts

Statistics
Hypothesis Testing
Two-sample t-test

Formulas

t = (X̄ - Ȳ) / sqrt((sX²/nX) + (sY²/nY))
Degrees of freedom (df) = ((sX²/nX + sY²/nY)²) / ((sX²/nX)²/(nX-1) + (sY²/nY)²/(nY-1))

Theorems

Central Limit Theorem
Student's t-distribution

Suitable Grade Level

Undergraduate