Suppose we wish to test $H _ { 0 } : \mu = 39$ vs. $H _ { \mathrm { a } } : \mu

Question

Suppose we wish to test $H _ { 0 } : \mu = 39$ vs. $H _ { \mathrm { a } } : \mu < 39$. Which of the following possible sample results gives the most evidence to support $H _ { \text {a } }$ (i.e., reject $H _ { 0 }$ )?
A) $\bar { x } = 36 , s = 6$
B) $\bar { x } = 37 , \mathrm {~s} = 4$
C) $\bar { x } = 35 , s = 3$
D) $\bar { x } = 35 , s = 7$

Quizplus · Accepted Answer

The most evidence to support $H_a$ (reject $H_0$) comes from the sample with the lowest mean ($\bar{x}$) and the smallest standard deviation (s), which indicates the most significant deviation from the null hypothesis mean ($\mu = 39$) with the least variability. Option C ($\bar{x} = 35, s = 3$) meets these criteria, suggesting the strongest evidence against $H_0$.

Suppose We Wish to Test H0:μ=39H _ { 0 } : \mu = 39H0​:μ=39

Suppose We Wish to Test $H _ { 0 } : \mu = 39$