Question

It is generally believed that the mean value of the district's total SAT score distribution is equal to 1200 (the null hypothesis). The principal from one of the schools claims that the mean value of the district's total SAT score distribution is not 1200. Perform the appropriate test with a 5% margin of error. What is the corresponding p-value?

Answer 1

The corresponding p-value, is p = 1

Explanation:

The maximum score SAT score, n = 1,600

The mean of the district's total SAT score distribution = 1,200

The claim of one of the districts principal, is the that mean of the district's total SAT score distribution ≠ 1,200

Using proportions, we have;

p = 1,200/1,600 = 0.75

q = 1 - p = 0.25

The margin of error, E = Z√(p·q/n)

∴ E = 5% = Z×√((0.75 × 0.25)/1,600)

z = 0.05/(√((0.75 × 0.25)/1,600)) ≈ 4.61880

Therefore, the corresponding p-value, p = 1