Given $n _ { 1 } = 14 , n _ { 2 } = 23 , \mathrm {~S} = 307 , \text { and } H _ { 1 } : m _ { 1 } m _ { 2 }$ compute z .
A) 0.74
B) 1.28
C) 17.95
D) 2.22

Question

Given $n _ { 1 } = 14 , n _ { 2 } = 23 , \mathrm {~S} = 307 , \text { and } H _ { 1 } : m _ { 1 } > m _ { 2 }$ compute  z .
A)  0.74 
B)  1.28 
C)  17.95 
D)  2.22

Quizplus · Accepted Answer

The z-score for a hypothesis test comparing two means can be calculated using the formula: $$z = \frac{(\bar{x}_1 - \bar{x}_2) - (\mu_1 - \mu_2)}{\sqrt{\frac{S^2}{n_1} + \frac{S^2}{n_2}}}$$ Given that $H_1: m_1 > m_2$, we assume $\mu_1 - \mu_2 = 0$ for the null hypothesis. Plugging in the given values: $n_1 = 14$, $n_2 = 23$, and $S = 307$, we get: $$z = \frac{0}{\sqrt{\frac{307^2}{14} + \frac{307^2}{23}}}$$ However, without the sample means ($\bar{x}_1$ and $\bar{x}_2$), we cannot directly calculate $z$ from the provided information. The correct calculation of $z$ involves using the actual difference between the sample means, which is not provided. Given the choices, the correct answer must be inferred based on typical statistical procedures or a misunderstanding in the question's presentation. Assuming a standard approach and typical values, a z-score of 1.28 is plausible for many standard statistical tests, indicating a moderate difference between groups. However, without the actual means or further clarification, this explanation relies on interpreting the provided information and common statistical outcomes.

Given n1=14,n2=23, S=307, and H1:m1>m2n _ { 1 } = 14 , n _ { 2 } = 23 , \mathrm {~S} = 307 , \text { and } H _ { 1 } : m _ { 1 } > m _ { 2 }n1​=14,n2​=23, S=307, and H1​:m1​>m2​

Given $n _ { 1 } = 14 , n _ { 2 } = 23 , \mathrm {~S} = 307 , \text { and } H _ { 1 } : m _ { 1 } > m _ { 2 }$