A study considers if the mean score on a college entrance exam for students in 2010 is any different from the mean score of 500 for students who took the same exam in 1985. Let μ represent the mean score for all students who took the exam in 2010. For a random sample of 25,000 students who took the exam in 2010, x = 498 and s = 100.
a. Show that the test statistic is t = -3.16.
b. Find the P-value for testing H0: μ = 500 against Ha: μ ≠ 500.
c. Explain why the test result is statistically significant but not practically significant.