Question

a study measuring fitness level in teens randomly sampled 112 male teens and 101 female teens with a higher score indicating more fitness. researchers suspected that the fitness level for male teens ($mu_1$) is higher than for female teens ($mu_2$), and wanted to check whether the data would supported this hypothesis.
the following hypotheses were tested:
$h_0:mu1 = mu2$
$h_a:mu1>mu2$

sample	n	mean	sd
2(f)	102	7.15	6.31

t - test of difference: df = 210 t - value = 0.25 p - value = 0.400
which of the following is an appropriate conclusion based on the output?
a. the data do not provide sufficient evidence to reject $h_0$, so we accept it, and conclude that female and male teens do not differ in mean fitness score.
b. the data provide sufficient evidence to conclude that male and female teens do not differ in mean fitness score.
c. the data provide sufficient evidence to reject $h_0$ and to conclude that the mean fitness score for male teens is higher than that of female teens.
d. the data do not provide sufficient evidence to conclude that the mean fitness score of male teens is higher than that of female teens.

Explanation:

Step1: Recall hypothesis - testing rule

In hypothesis - testing, if the p - value is greater than the significance level (commonly $\alpha = 0.05$), we fail to reject the null hypothesis $H_0$.

Step2: Analyze given p - value

Here, the p - value is $0.400$. Since $0.400>0.05$, we fail to reject the null hypothesis $H_0:\mu_1=\mu_2$. This means we do not have enough evidence to support the alternative hypothesis $H_a:\mu_1 > \mu_2$.

Answer:

D. The data do not provide sufficient evidence to conclude that the mean fitness score of male teens is higher than that of female teens.