Question

A report criticizes SAT-test-preparation providers for promising big score gains without any hard data to back up such claims (The Wall Street Journal, May 20, 2009). Suppose eight college-bound students take a mock SAT, complete a three-month test-prep course, and then take the real SAT.

Student	Mock SAT			Real SAT
1		1830			1840
2		1760			1800
3		2000			2010
4		2150			2190
5		1630			1620
6		1840			1960
7		1930			1890
8		1710			1780

Let the difference be defined as scores on Mock SAT – Real SAT, and assume that the difference is normally distributed.

a. Specify the competing hypotheses that determine whether completion of the test-prep course increases a student’s score, on average, on the real SAT.

• H₀: μ_D = 0; H_A: μ_D ≠ 0

• H₀: μ_D ≥ 0; H_A: μ_D < 0

• H₀: μ_D ≤ 0; H_A: μ_D > 0

b. Calculate the value of the test statistic. (Negative value should be indicated by a minus sign. Round final answer to 3 decimal places.)

c. Find the p-value.

• p-value < 0.01

• 0.01 ≤ p-value < 0.025

• 0.025 ≤ p-value < 0.05

• 0.05 ≤ p-value < 0.10

• p-value ≥ 0.10

d. At the 5% significance level, do the sample data support the test-prep providers’ claims?

• Yes,since we reject H₀.

• No, since we reject H₀.

• Yes, since we do not reject H₀.

• No, since we do not reject H₀.

Answer 1