A study of methods for teaching reading in the third grade was conducted. A classroom of 21 students participated in directed reading activities for eight weeks. Another classroom, with 23 students, followed the same curriculum without the activities. Students in both classrooms then took the same reading test. The scores of the two groups are shown in the back-to-back stem-and-leaf plot.

At α = 0.05, is there enough evidence to support the claim that third graders taught with the directed reading activities scored higher than those taught without the activities? Assume the population variances are equal.

(a) Identify the claim and state H₀ and H_a,

(b) Find the critical value(s) and identify the rejection region(s),

(c) Find the standardized test statistic t,

(d) Decide whether to reject or fail to reject the null hypothesis,

(e) Interpret the decision in the context of the original claim. Assume the samples are random and independent, and the populations are normally distributed. If convenient, use technology.

Classroom With Activities Classroom Without Activities 1 0 7 9 4 2 0 68 3 3 377 9 9 6 4 3 33 41 2 2 2 3 6 8 9 8 7 76 4 3 2 5 3 4 5 5 721 6 0 2 Key: 4 210 24 for classroom with activities and 20 for classroom without activities