Given $n _ { 1 } = 18 , n _ { 2 } = 27 , \mathrm {~S} = 398 , \text { and } H _ { 1 } : m _ { 1 }

Question

Given $n _ { 1 } = 18 , n _ { 2 } = 27 , \mathrm {~S} = 398 , \text { and } H _ { 1 } : m _ { 1 } < m _ { 2 }$ compute $\sigma _ { S }$
A) 43.16
B) 414
C) 56
D) -0.37

Quizplus · Accepted Answer

$\sigma _ { S } = \sqrt { n _ { 1 } n _ { 2 } S / ( n _ { 1 } + n _ { 2 } ) ^ { 2 } } = \sqrt { 18 \times 27 \times 398 / ( 18 + 27 ) ^ { 2 } } = \sqrt { 486 \times 398 / 2025 } = \sqrt { 193428 / 2025 } = \sqrt { 95.6 } \approx 9.78.$ The correct calculation for $\sigma _ { S }$ should yield a result close to 9.78, indicating a mistake in the provided options.

Given n1=18,n2=27, S=398, and H1:m1<m2n _ { 1 } = 18 , n _ { 2 } = 27 , \mathrm {~S} = 398 , \text { and } H _ { 1 } : m _ { 1 } < m _ { 2 }n1​=18,n2​=27, S=398, and H1​:m1​<m2​

Given $n _ { 1 } = 18 , n _ { 2 } = 27 , \mathrm {~S} = 398 , \text { and } H _ { 1 } : m _ { 1 } < m _ { 2 }$