Question

An instructor gave students the option to purchase an interactive program that allows them to answer questions during class and receive credit for participating. Alternatively, students could work an extra problem during weekly homework assignments. The instructor randomly selected 10 students, then randomly divided them into two groups of five each. One group was provided the interactive tool, the other group was asked to work the extra problem. The instructor knew from prior experience that the interactive tool increases attendance. The table displayed contains the final exam scores for the 10 students, on a scale from 0 to 100. Interactive 65 78 84 88 96 Extra problem 56 61 70 75 82 The instructor wishes to test whether increased attendance throughout the semester leads to improved exam scores. Let μ I = mean score that would be observed if all students used the interactive tool and μ E = mean score if all students worked an extra problem. For testing H 0 : μ I = μ E , it has been suggested in the past to use a version of the t test that calculates a pooled variance estimate. Such an assumption requires that:

the population standard deviations σ 1 and σ 2 be equal. the sample means ¯ x 1 x ¯ 1 and ¯ x 2 x ¯ 2 be equal.

the sample standard deviations s 1 s 1 and s 2 s 2 be equal.

the population means μ 1 μ 1 and μ 2 μ 2 be equal.

Answer 1