EXAMPLE 7.13

Is there an improvement? For the DRP study described in Example 7.11 (page 437), we hope to show that the treatment (Group 1) performs better than the control (Group 2). For a formal significance test, the hypotheses are

H₀: μ₁ = μ₂

H_a: μ₁ >μ₂

The two-sample t test statistic is

= 2.31

The P-value for the one-sided test is P(T ≥ 2.31). For the second approximation, the degrees of freedom k are equal to the smaller of

n₁ − 1 = 21 − 1 = 20  and  n₂ − 1 = 23 − 1 = 22

Comparing 2.31 with the entries in Table D for 20 degrees of freedom, we see that P lies between 0.01 and 0.02.

The data strongly suggest that directed reading activity improves the DRP score (t = 2.31, df = 20, 0.01 < P < 0.02).