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Lab 20 Worksheet
Question 1
(1) A psychologist is interested in studying the effects of fatigue on mental alertness. She
decides to study this question using an independent samples design. She randomly
assigns individuals to two groups.


Group 1 stays awake for 24 hours
Group 2 gets to go to sleep
After this period, each subject is tested to see how well they detect a light on screen (the
dependent variable is the subjects' number of mistakes which reflects their mental
alertness. So the higher the number, the less alert they are.).
Here are the results from the two groups:
Group 1 Group 2
Means
35
24
SS
120
270
n
5
10
You will use an independent samples t-test, to answer the question of whether fatigue
affects mental alertness (α = 0.05). This is a 2-tailed test.
Question 1.1: What is the null hypothesis?
Question 1.2: What are the degrees of freedom in both groups?
Question 1.3: What is the total degrees of freedom?
Question 1.4: What is the pooled variance?
Question 1.5: What is the estimated standard error?
Question 1.6: What is the estimated standard error?
Question 1.7: If the null hypothesis is true, what is the population mean of the difference
between the sample means?
Question 1.8: What is the critical value of t?
Question 1.9: What is the observed value of t?
Question 1.10: Should you reject or fail to reject the null hypothesis?
Question 1.11: State your conclusion about the results in ordinary language.
Question 2
A biology instructor at a large university teaches a class of 22 students who attend 2
different lab sections. Each group is given different modes of instruction. One group is
given a standard lab section whereas the other has a lab enhanced with online videos. The
instructor is concerned about evaluating the two groups of students with the same scale,
given the differences in their lab experiences. The data below are the scores of the
students on the first midterm. He wants to know if there is a difference between how the
two groups scored. Assume that α = 0.05. The data are as follows (notice that one group
has more students than the other):
Try copying and pasting the numbers directly into SPSS!
Student Exam scores Lab
1
60
1
2
65
1
3
69
1
4
58
1
5
57
1
6
59
1
7
52
1
8
72
1
9
70
1
10
65
1
11
70
2
12
85
2
13
72
2
14
83
2
15
81
2
16
69
2
17
65
2
18
75
2
19
79
2
20
71
2
21
89
2
22
80
2
Question 2.1: What is the null hypothesis?
Question 2.2: What are the degrees of freedom in both groups?
Question 2.3: What is the total degrees of freedom?
Question 2.4: What is the pooled variance?
Question 2.5: What is the estimated standard error?
Question 2.6: What is the estimated standard error?
Question 2.7: If the null hypothesis is true, what is the population mean of the difference
between the sample means?
Question 2.8: What is the critical value of t?
Question 2.9: What is the observed value of t?
Question 2.10: Should you reject or fail to reject the null hypothesis?
Question 2.11: State your conclusion about the results in ordinary language.
Question 3
Consider the following set of headache intensity data from a clinical trial for 2 different
types of headache medicine:
Person
Headache Intensity
Treatment
1
10
1
2
2
1
3
1
1
4
15
1
5
7
1
6
11
2
7
5
2
8
2
2
9
18
2
10
9
2
Question 3.1: Are the 2 types of treatment significantly different from each other?
Question 3.2: Now assume that the same data are from a repeated-measures design using
one sample of 5 subjects, each of whom have been tested twice. Use SPSS to do a pairedsamples t-test to see whether the data indicate a significant difference between the two
treatments (again assume α = .05). Remember that you'll have to change the way the data
are entered in the data window. It should like something like this:
Person Treatment 1 Treatment 2
1
10
11
2
2
5
3
1
2
4
15
18
5
7
9
Are the 2 types of treatment significantly different from each other?
Question 3.3: Why are the results different for the different types of t-tests? Hint: The
numerators are exactly the same in the paired-samples t-test and independent-samples ttest so the difference has to come from the denominators.
Review Questions
4. Suppose you conduct a 1-sample t-test with α = .05. Your p value is .044. Should you
reject the null hypothesis?
5. Find the correlation between X and Y
X
10
6
9
4
3
2
Y
7
2
4
6
5
1
6. In a population with scores of µ = 124 and σ = 54. If we randomly select 98 scores,
what is the probability that the sample mean would be between 30 and 45?
7. Suppose we test 85 people with a known population standard deviation of σ = 12. The
sample mean was 57. Estimate the upper bound of the 99% confidence interval for the
population mean.
8. When using SPSS, the P value (or Sig. value) must be less than or equal to what in
order to reject the null hypothesis?
9. What kind of test would you use when you want to see if a sample mean came from a
certain population and you know the population mean but you don’t know the population
standard deviation?
10. With a paired-samples t-test, what does D represent?
11. Does a one-sample t-test test the null or alternative hypothesis?
12. If you had all the information necessary to conduct either a 1-sample t-test or a z-test,
why should you always choose the z-test?