Answer:
The correct option is (D).
Step-by-step explanation:
The <em>p</em>-value is well defined as per the probability, [under the null hypothesis (<em>H₀</em>)], of attaining a result equivalent to or more extreme than what was truly observed.
A small <em>p</em>-value (typically ≤ 0.05) specifies solid proof against the null hypothesis (<em>H₀</em>), so you discard <em>H₀</em>.
A large <em>p</em>-value (> 0.05) specifies fragile proof against the <em>H₀</em>, so you fail to discard <em>H₀</em>.
The hypothesis is defined as follows:
<em>H₀</em>: The slope of the regression line is 0, i.e. <em>β </em>= 0.
<em>Hₐ</em>: The slope of the regression line is greater than 0, i.e. <em>β </em>> 0.
A scatter-plot of the measurements taken from 18 randomly selected college athletes displayed a strong positive linear relationship between the two variables; lean body mass and maximal oxygen uptake.
The significance level of the test is, <em>α</em> = 0.05.
The <em>p</em>-value of the test is, <em>p</em>-value = 0.04
As the <em>p</em>-value = 0.04 < <em>α</em> = 0.05, we reject the null hypothesis.
So, it can be concluded that there is a statistical evidence of a relationship between lean body mass and maximal oxygen uptake for college athletes.
Since the scatter-plot shows a strong positive linear relationship, it implies that as the an increase in lean body mass causes an increase in maximal oxygen uptake for college athletes.
Thus, the correct option is (D).
