Question

Before taking an exam, students either went to bed at their normal times or were sleep deprived for 4 to 8 hours. Half of each group were given a caffeine pill before taking the exam. Determine the number of factors, levels for each, and number of treatments.

Answer 1

The experiment involves two factors: sleep deprivation and caffeine intake. There are four treatments overall: normal sleep without caffeine, normal sleep with caffeine, sleep deprived without caffeine, sleep deprived with caffeine.

Step-by-step explanation:

The experiment described involves two groups of students: one group that went to bed at their normal times and another group that was sleep deprived for 4 to 8 hours before taking the exam. Each group was further divided into two halves, with one half being given a caffeine pill before the exam. Therefore, there are two factors in this experiment: sleep deprivation (with two levels: normal sleep and sleep deprived) and caffeine intake (with two levels: caffeine pill and no pill). The number of treatments is four (normal sleep without caffeine, normal sleep with caffeine, sleep deprived without caffeine, sleep deprived with caffeine).

Answer 2

In this experimental design, there are two factors: Sleep Condition and Caffeine. Each factor has two levels. The total number of treatments is 4, and each treatment represents a combination of one level from each factor.

To determine the number of factors, levels for each factor, and the number of treatments in this experimental design, we can break down the information provided step by step:

1. Factors:

- Factor 1: Sleep Condition (Normal Sleep vs. Sleep Deprived)

- Factor 2: Caffeine (With Caffeine Pill vs. Without Caffeine Pill)

2. Levels for Each Factor:

- Factor 1 (Sleep Condition):

- Level 1: Normal Sleep

- Level 2: Sleep Deprived

- Factor 2 (Caffeine):

- Level 1: With Caffeine Pill

- Level 2: Without Caffeine Pill

3. Number of Treatments:

To determine the number of treatments, multiply the number of levels for each factor. In this case, we have 2 levels for Factor 1 and 2 levels for Factor 2.

Number of treatments = Number of levels for Factor 1 × Number of levels for Factor 2

Number of treatments = 2 (levels for Factor 1) × 2 (levels for Factor 2) = 4 treatments