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
4636
Mean = Mean =
S = S =
S2 = S2 =


  1. What is your computed answer?

  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 is your tcrit?

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

  7. Interpret your answer.

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



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
77
3 4
11 14
8 6
5 7
14 12
7 5
9 5
108
Mean = Mean =
S = S =
S2 = S2 =

  1. What is your computed answer?

  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?

  7. Interpret your answer.

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


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
2914
Mean = Mean =
S = S =
S2 = S2 =
  1. What is your computed answer?

  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 is your tcrit?

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

  7. Interpret your answer.

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


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
832
Mean = Mean =
S = S =
S2 = S2 =
  1. What is your computed answer?

  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?

  7. Interpret your answer.

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


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 = 8.6Mean = 7.6
S = 3.306559138 S = 3.169297153
S2 = 10.933333333S2 = 10.044444444

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

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

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