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) / √[(s_X^2 / n_X) + (s_Y^2 / n_Y)]
Degrees of freedom (df) = [(s_X^2 / n_X + s_Y^2 / n_Y)^2] / [(s_X^2 / n_X)^2 / (n_X - 1) + (s_Y^2 / n_Y)^2 / (n_Y - 1)]

Theorems

Welch's t-test
Central Limit Theorem

Suitable Grade Level

Undergraduate Statistics