Question

Suppose you are interested in whether the GPAs of college athletes are significantly different from the GPAs of the college athlete population. To investigate this, you obtain a random sample of academic records of 5 athletes and compare their GPA to the known student population.

Here are your data:

Student Athletes	Entire Student Population
Mean = 3.02	Mean = 2.8
s = .8

Using an alpha = .05, what is your alternative/research hypothesis?

Answer 1

Data Summary

	Mean (M)	Sample Size (n)	Standard Deviation (SD)
Population	2.8     (μ)
Sample	3.02     (X̅)	5      (n)	0.8     (s)

α = 0.05

Since it is required to test if GPAs of college athletes are significantly different from the GPAs of the college population

the null and alternative hypotheses are

Ho : μ = 2.8                                    where μ is the population mean GPA of college students
Ha : μ ≠ 2.8

Using the formula given below, we get the test statistic

  
t-statistic = 0.6149     
     
Degrees of Freedom     
df = n - 1 = 4     
For t = 0.6149 df = 4 we find the Two Tailed p-value using Excel function t.dist     
     
p-value = T.DIST.2T(0.6149,4)     
p-value = 0.5719     
     
Decision     
0.5719 > 0.05     
that is p-value > α     
Hence we DO NOT REJECT Ho     
     
Conclusion
There does not exist enough statistical evidence at α = 0.05 to show that

the GPAs of college athletes are significantly different from the GPAs of the college student population