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25-04-2024
Mathematics

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Among the data collected for the World Health Organization air quality monitoring project is a measure of suspended particles in μg/m³ . Let X and Y equal the concentration of suspended particles in μg/m³ in the city center (commercial district) for Melbourne and Houston, respectively. Using n = 13 observations of X and m = 16 observations of Y , we test H₀ : μ X = μ Y against H 1 : μ X < μ Y . (a) Define the test statistic and critical region, assuming normal population distributions with unknown but equal variance. Let ↵ = 0 . 05. (b) If x = 72 . 9 , s x = 25 . 6 , y = 81 . 7, and sᵧ = 28 . 3, calculate the value of the test statistic and state your conclusion.

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