Question

assume that you have a sample of ( n_1 = 8 ), with the sample mean ( \bar{x}_1 = 46 ), and a sample standard deviation of ( s_1 = 7 ), and you have an independent sample of ( n_2 = 4 ) from another population with a sample mean of ( \bar{x}_2 = 39 ) and the sample standard deviation ( s_2 = 8 ). assuming the population variances are equal, at the 0.01 level of significance, is there evidence that ( mu_1 > mu_2 )?
determine the hypotheses. choose the correct answer below.
a. ( h_0: mu_1=mu_2 )
( h_1: mu_1
eqmu_2 )
b. ( h_0: mu_1
eqmu_2 )
( h_1: mu_1=mu_2 )
c. ( h_0: mu_1>mu_2 )
( h_1: mu_1leqmu_2 )
d. ( h_0: mu_1leqmu_2 )
( h_1: mu_1>mu_2 )

Explanation:

In hypothesis testing for comparing two population means ($\mu_1$ and $\mu_2$), the null hypothesis ($H_0$) is a statement of no difference or a specific relationship (in this case, non - superiority). The alternative hypothesis ($H_1$) is what we are trying to find evidence for. Since we want to test if $\mu_1>\mu_2$, the null hypothesis should be the opposite (a non - superior relationship, i.e., $\mu_1\leq\mu_2$) and the alternative hypothesis is $\mu_1 > \mu_2$.

Answer:

D. $H_0:\mu_1\leq\mu_2$; $H_1:\mu_1 > \mu_2$