Ga university administrator obtains a sample of the academic records of past and present scholarship athletes at the university. the administrator reports that no significant difference was found in the mean gpa (grade point average) for male and female scholarship athletes (p = 0.287). this conclusion implies that the maximum difference in gpas between male and female scholarship athletes is 0.287. the chance of obtaining a difference in gpas between male and female scholarship athletes as large as that observed in the sample if there is no difference in mean gpas is 0.287. the gpas for male and female scholarship athletes are identical, except for 28.7% of the athletes. the chance that a pair of randomly chosen male and female scholarship athletes would have a significant difference in gpas is 0.287

the chance of obtaining a difference in GPAs between male and female scholarship athletes as large as that observed in the sample if there is no difference in mean GPAs is 0.287

Step-by-step explanation:

When conducting hypothesis tests, the P value tells you the probability of the results happening by random chance.  That's why we usually test against a very low alpha level, usually 1% or 5%.  

Here P = 28%, so there is a 28% chance that if we take a sample of athletes, about 1 out of 4 times there won't be a significant difference in GPA between males and females.

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below: