Question

Laptops and other digital technologies with wireless access to the Internet are becoming more and more common in the classroom. While numerous studies have shown that these technologies can be used effectively as part of teaching, there is concern that these technologies can also distract learners if used for off-task behaviors. In one study that looked at the effects of off-task multitasking with digital technologies in the classroom, a total of 145 undergraduates were randomly assigned to one of seven conditions.7 Each condition involved a task that was conducted simultaneously with a class lecture. The study consisted of three 20-minute lectures, each followed by a 15-item quiz. The following table summarizes the conditions and quiz results.

Lecture 3 Lecture 2 Lecture 1 Condition 0.57 0.75 0.56 21 Texting 0.50 0.43 0.52 0.69 20 Email 0.50 20 0.68 Facebook MSN Messaging 0.42 0.71 0.48 21 0.50 0.58 0.78 21 Natural use control Word-processing control 21 Paper-and-pencil control 21 0.75 0.57 0.55 0.53 0.60 0.74 th enn af thu th5ee cuvizz.ar ar tha tesnonse Comn

Refer to the previous exercise. Let μ1, μ2, ... , μ7 represent the mean scores for the 7 conditions. The first 4 conditions refer to off-task behaviors, while the last 3 conditions represent different sorts of controls. (a) The researchers hypothesized that the average score for the off-task behaviors would be lower than that for the paper-and-pencil control condition. Write a contrast that expresses this comparison. (b) For this contrast, give H0 and an appropriate Ha.

Answer 1

(a)required contrast c=(μ1+μ2+μ3+μ4)/4 -μ7

Contrast is a linear combination of variables such that sum of all the coefficients would be zero.

Here sum of coefficient is (1/4+1/4+1/4+1/4)-1=0

(b) Null hypothesis H0:(μ1+μ2+μ3+μ4)/4 -μ7 $\ge$0 and

alternate hypothesis Ha:(μ1+μ2+μ3+μ4)/4 -μ7< 0

since we want to test average score for the off-task behaviors ((μ1+μ2+μ3+μ4)/4) would be lower than that for the paper-and-pencil control condition (μ7), so :(μ1+μ2+μ3+μ4)/4 -μ7< 0 would be alternate hypothesis and opposite of it would (μ1+μ2+μ3+μ4)/4 -μ7 $\ge$​​​​​​​0 be null hypothesis