## Practice Problems: t-tests

Sleep researchers decide to test the impact of REM sleep deprivation on a computerized assembly line task. Subjects are required to participate in two nights of testing. On the nights of testing EEG, EMG, EOG measures are taken. On each night of testing the subject is allowed a total of four hours of sleep. However, on one of the nights, the subject is awakened immediately upon achieving REM sleep. On the alternate night, subjects are randomly awakened at various times throughout the 4 hour total sleep session. Testing conditions are counterbalanced so that half of the subject experience REM deprivation on the first night of testing and half experience REM deprivation on the second night of testing. Each subject after the sleep session is required to complete a computerized assembly line task. The task involves five rows of widgets slowly passing across the computer screen. Randomly placed on a one/five ratio are widgets missing a component that must be "fixed" by the subject. Number of missed widgets is recorded. Compute the appropriate t-test for the data provided below.

 REM Deprived Control Condition D D2 26 20 6 36 15 4 11 121 8 9 -1 1 44 36 8 64 26 20 6 36 13 3 10 100 38 25 13 169 24 10 14 196 17 6 11 121 29 14 15 225 Mean = 24.0 Mean = 14.7 D = 93 D2 = 1069 S = 11.23486636 S = 10.53090689 S2 = 126.22222222 S2 = 110.9

### Correlated t-test

2. What would be the null hypothesis in this study? Lack of REM sleep will have no impact on performance of a computer assemply line task; scores will not be any better or any worse.

3. What would be the alternate hypothesis? Lack of REM sleep will impact performance on a computer assembly line task; scores will either be significantly better or worse.

4. What probability level did you choose and why? .05 In this case, I would be concerned about making a Type II error. I would not want to say that lack of REM sleep has no impact on one's performance and then later find out I was wrong.

5. What is your tcrit? tcrit = 2.262

6. Is there a significant difference between the two testing conditions? Yes, performance was significantly lower after REM deprivation; the subjects make significantly more errors.

7. Interpret your answer. REM deprivation appears to significantly reduce performance on a computer assembly line task (t=6.175, p < .001). You will notice that I reported the .001 as even at this level, the tobs was still in the tail.

8. If you have made an error, would it be a Type I or a Type II error? Explain your answer. If an error was made, it would have to be a Type I error. I found a difference when it may be that REM deprivation really has no impact on computerized assembly line performance. I may just have a bizarre sample.

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