Question

has developed a new way of teaching story problems in sixth grade 8. Mary arithmetic. She used her method on a random sample of 15 sixth grad taught to solve story problems by a traditional method ers from her school. An independent random sample of 12 sixth graders were . All students were given the same test. Is there evidence that the new method result in improves performance on story problems? Use a 5% significance level. method158 8.5 10.0 New method Traditional Method 12 75 Since these are small sample sizes, what shape do we need to assume for t the distribution of,? 19. Using the inf ormation above, find and interpret a 95% confidence interval for the difference of the means?

Answer 1

?₁ - ?₂ = (M₁ - M₂) = 7

Standard Error
s_{(M1 - M2)} = ?((s²_p/n₁) + (s²_p/n₂)) = ?((84.46/15) + (84.46/12)) = 3.56

Confidence Interval
?₁ - ?₂ = (M₁ - M₂) ± ts_{(M1 - M2)} = 7 ± (2.06 * 3.56) = 7 ± 7.33

Result

?₁ - ?₂ = (M₁ - M₂) = 7, 95% CI [-0.33, 14.33].

You can be 95% confident that the difference between your two population means (?₁ - ?₂) lies between -0.33 and 14.33.