Question

question 1
a canadian study measuring depression level in teens (as reported in the journal of adolescence, vol. 25, 2002) randomly sampled 112 male teens and 101 female teens, and scored them on a common depression scale (higher score representing more depression). the researchers suspected that the mean depression score for male teens is higher than for female teens, and wanted to check whether data would support this hypothesis.
if $mu_1$ and $mu_2$ represent the mean depression score for male teens and female teens respectively, which of the following is an appropriate pair of hypotheses in this case? check all that apply.
a.
$h_0:mu_1 - mu_2=0$
$h_a:mu_1 - mu_2<0$
b.
$h_0:mu_1 - mu_2>0$
$h_a:mu_1 - mu_2=0$
c.
$h_0:mu_1=mu_2$
$h_a:mu_1>mu_2$
d.
$h_0:mu_1 - mu_2=0$
$h_a:mu_1 - mu_2>0$

Explanation:

Step1: Define null and alternative hypotheses

The null hypothesis ($H_0$) is a statement of no - effect or no difference. The alternative hypothesis ($H_a$) is what we are trying to find evidence for. Here, the researchers suspect that the mean depression score for male teens ($\mu_1$) is higher than for female teens ($\mu_2$).

Step2: Analyze each option

• Option A: $H_0:\mu_1-\mu_2 = 0$ and $H_a:\mu_1 - \mu_2<0$ is wrong because the alternative hypothesis should be $\mu_1-\mu_2>0$ if we suspect $\mu_1>\mu_2$.
• Option B: The null hypothesis and alternative hypothesis are reversed. The null hypothesis should be a statement of equality.
• Option C: $H_0:\mu_1=\mu_2$ (equivalent to $\mu_1 - \mu_2=0$) and $H_a:\mu_1>\mu_2$ (equivalent to $\mu_1 - \mu_2>0$) is correct as it states no difference in the null and the suspected difference in the alternative.
• Option D: $H_0:\mu_1-\mu_2 = 0$ and $H_a:\mu_1-\mu_2>0$ is also correct as it follows the standard form of null and alternative hypotheses for testing if $\mu_1>\mu_2$.

Answer:

C. $H_0:\mu_1=\mu_2$, $H_a:\mu_1>\mu_2$
D. $H_0:\mu_1 - \mu_2=0$, $H_a:\mu_1-\mu_2>0$