## Practice Problems: t-tests

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A research study was conducted to examine the differences between older and younger adults on perceived life satisfaction. A pilot study was conducted to examine this hypothesis. Ten older adults (over the age of 70) and ten younger adults (between 20 and 30) were give a life satisfaction test (known to have high reliability and validity). Scores on the measure range from 0 to 60 with high scores indicative of high life satisfaction; low scores indicative of low life satisfaction. The data are presented below. Compute the appropriate t-test.

 Older Adults Younger Adults 45 34 38 22 52 15 48 27 25 37 39 41 51 24 46 19 55 26 46 36 Mean = Mean = S = S = S2 = S2 =

2. What would be the null hypothesis in this study?

3. What would be the alternate hypothesis?

4. What probability level did you choose and why?

6. Is there a significant difference between the two groups?

8. If you have made an error, would it be a Type I or a Type II error? Explain your answer.

A researcher hypothesizes that electrical stimulation of the lateral habenula will result in a decrease in food intake (in this case, chocolate chips) in rats. Rats undergo stereotaxic surgery and an electrode is implanted in the right lateral habenula. Following a ten day recovery period, rats (kept at 80 percent body weight) are tested for the number of chocolate chips consumed during a 10 minute period of time both with and without electrical stimulation. The testing conditions are counter balanced. Compute the appropriate t-test for the data provided below.

 Stimulation No Stimulation 12 8 7 7 3 4 11 14 8 6 5 7 14 12 7 5 9 5 10 8 Mean = Mean = S = S = S2 = S2 =

2. What would be the null hypothesis in this study?

3. What would be the alternate hypothesis?

4. What probability level did you choose and why?

5. What were your degrees of freedom?

6. Is there a significant difference between the two testing conditions?

8. If you have made an error, would it be a Type I or a Type II error? Explain your answer.

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 26 20 15 4 8 9 44 36 26 20 13 3 38 25 24 10 17 6 29 14 Mean = Mean = S = S = S2 = S2 =

2. What would be the null hypothesis in this study?

3. What would be the alternate hypothesis?

4. What probability level did you choose and why?

6. Is there a significant difference between the two testing conditions?

8. If you have made an error, would it be a Type I or a Type II error? Explain your answer.

Researchers want to examine the effect of perceived control on health complaints of geriatric patients in a long-term care facility. Thirty patients are randomly selected to participate in the study. Half are given a plant to care for and half are given a plant but the care is conducted by the staff. Number of health complaints are recorded for each patient over the following seven days. Compute the appropriate t-test for the data provided below.

 Control over Plant No Control over Plant 23 35 12 21 6 26 15 24 18 17 5 23 21 37 18 22 34 16 10 38 23 23 14 41 19 27 23 24 8 32 Mean = Mean = S = S = S2 = S2 =

2. What would be the null hypothesis in this study?

3. What would be the alternate hypothesis?

4. What probability level did you choose and why?

5. What are your degrees of freedom?

6. Is there a significant difference between the two groups?

8. If you have made an error, would it be a Type I or a Type II error? Explain your answer.

### Means, Standard Deviations, and Variances for the Problems Provided Above

 1. Older Adults Younger Adults Mean = 44.5 Mean = 28.1 S = 8.682677518 S = 8.543353492 S2 = 75.388888888 S2 = 72.988888888

 2. Stimulation No Stimulation Mean = 8.6 Mean = 7.6 S = 3.306559138 S = 3.169297153 S2 = 10.933333333 S2 = 10.044444444

 3. REM Deprived Control Condition Mean = 24.0 Mean = 14.7 S = 11.23486636 S = 10.53090689 S2 = 126.22222222 S2 = 110.9

 4. Control over Plant No Control over Plant Mean = 16.6 Mean = 27.066666666 S = 7.790103612 S = 7.741047056 S2 = 60.68571429 S2 = 59.92380952

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