Given $n _ { 1 } = 15 , n _ { 2 } = 25 , \mathrm {~S} = 320.5 \text {, and } H _ { 1 } : \mu _ { 1 } \neq \mu _ { 2 }$ compute $\mu _ { s ^ { } }$
A) 338
B) 0.36
C) 307.5
D) 35.79

Question

Given $n _ { 1 } = 15 , n _ { 2 } = 25 , \mathrm {~S} = 320.5 \text {, and } H _ { 1 } : \mu _ { 1 } \neq \mu _ { 2 }$ compute $\mu _ { s ^ {  } }$
A) 338
B)  0.36 
C)  307.5 
D)  35.79

Quizplus · Accepted Answer

$\mu _ { s ^ {  } }$ is the combined mean of two groups. It is calculated as $\mu _ { s ^ {  } } = \frac { n _ { 1 } \mu _ { 1 } + n _ { 2 } \mu _ { 2 } } { n _ { 1 } + n _ { 2 } }$. Given that $S = 320.5$ is the sum of all observations from both groups, and $n _ { 1 } + n _ { 2 } = 40$, the combined mean is $\mu _ { s ^ {  } } = \frac { S } { n _ { 1 } + n _ { 2 } } = \frac { 320.5 } { 40 } = 8.0125$. However, without the individual means $\mu _ { 1 }$ and $\mu _ { 2 }$, we cannot directly calculate $\mu _ { s ^ {  } }$ as intended in the options provided. The correct approach involves the total sum $S$ and the total count $n_1 + n_2$, but the calculation provided here does not match any of the options directly due to a misunderstanding in the interpretation of the given data and the question's intent. The correct calculation should involve understanding that $S$ represents a sum or a combined statistic rather than directly leading to the mean without the individual group means or the context implying a different calculation method. Given the options and the typical understanding of such problems, there seems to be a mistake in the explanation process. The correct answer should be based on the information provided and the usual statistical formulas, but with the given data, a direct calculation as shown doesn't align with the options, indicating a need for clarification or correction in the explanation approach.

Given n1=15,n2=25, S=320.5, and H1:μ1≠μ2n _ { 1 } = 15 , n _ { 2 } = 25 , \mathrm {~S} = 320.5 \text {, and } H _ { 1 } : \mu _ { 1 } \neq \mu _ { 2 }n1​=15,n2​=25, S=320.5, and H1​:μ1​=μ2​

Given $n _ { 1 } = 15 , n _ { 2 } = 25 , \mathrm {~S} = 320.5 \text {, and } H _ { 1 } : \mu _ { 1 } \neq \mu _ { 2 }$