Independent and Paired Sample t-Tests
Exercise for Chapter 21
Factual Questions
1. Example 1 mentions how many possible explanations for the 3-point difference?
2. What is the name of the hypothesis which states that the observed difference is due to
sampling errors created by random sampling?
3. Which of the following statements is true (circle one)?
A. The t test is used to test the difference between two sample means to determine
statistical significance.
B. The t test is used to test the difference between two population means to determine
statistical significance.
4. If a t test yields a low probability, such as p < .05, what decision is usually made about
the null hypothesis?
5. The larger the sample, the (circle one)
A. more likely the null hypothesis will be rejected.
B. less likely the null hypothesis will be rejected.
6. The smaller the observed difference between two means, the (circle one)
A. more likely the null hypothesis will be rejected.
B. less likely the null hypothesis will be rejected.
7. If there is no variation among members of a population, is it possible to have sampling
errors when sampling from the population?
8. If participants are first paired before being randomly assigned to experimental and control
groups, are the resulting data “independent” or “dependent”?
9. Which type of data tends to have less sampling error (circle one)?
A. Independent
B. Dependent
Exercise for Chapter 22
Factual Questions
1. What is the scenario when performing an Independent Samples t Test is required?
2. Assume that a researcher interested in growth spurts among young teens decided to measure the height difference between boys and girls in middle school from a random sample of 200 boys and girls. In this study, what are the two variables of interest and which of the two variables is the independent variable and the other, the dependent variables?
3. In the above scenario, state the null and the alternative hypotheses.
4. If alternative hypothesis is as follows: H A:
1
2, and you rejected the null hypothesis
in favor of the alternative hypothesis, state in words what you would conclude.
5. The above alternative hypothesis would be (circle one)?
A. Nondirectional hypothesis
B. Directional hypothesis
6. In another study, if the alternative hypothesis is
1 <
2 , and you concluded in favor of
the alternative hypothesis, in words what you would conclude?
7. The above alternative hypothesis would be (circle one)?
A. Nondirectional hypothesis
B. Directional hypothesis
8. Generally, the larger the samples, the smaller the standard errors become, increasing the
likelihood of finding statistical significance. This statement is (circle one)?
A. True
B. False
9. Calculating the standard error of the difference between means depends on the standard
deviations as well as the sample sizes between the groups, and can be considered equal
or unequal. This statement is (circle one)?
A. True
B. False
10. What do the following results indicate in terms of rejecting the null hypothesis: (t = 3.20,
df = 28, p < .05, two-tailed test)?
Question for Discussion
11. Give an example of one continuous data and one categorical data with two categories that
would require performing an Independent Samples t Test
Exercise for Chapter 23
Factual Questions
1. How is the Dependent Samples t Test different from Independent Samples t Test in terms
of samples?
2. What are the similarities in the assumptions behind both the Dependent and Independent
Samples t Test?
3. What is Dependent Samples t Test with one sample also known as?
4. In a Dependent Samples t Test what is the df for a sample of 100 participants in a particular
study?
5. The Dependent Samples t Test would have less sampling error in its design. Discuss the
reasons.
6. Given the results below what would you conclude about the mean difference between Group
A and Group B?
Group Number Cor. P Mean SD SE of
of Pairs Mean
Group A 50 .087 .549 7.64 1.03 .145
Group B 4.82 1.32 .187
Paired difference
Mean SD SE of T Value df P
Difference Mean
Question for Discussion
7. Give an example of one continuous data and one categorical data
with two categories that would require performing a Dependent
Samples t Test
Exercise for Chapter 24
Factual Questions
1. Which of the following statements is true (circle one)?
A. One Sample t Test is used to test the difference between a sample mean and a
population mean to determine statistical significance
B. One Sample t Test is used to test the difference between two sample means from
one sample.
2. SAT verbal scores are normally distributed with the population mean of 500. A local high
school has instituted a new program to engage students in reading. A sample of 90 students
from this high school is randomly selected following their participation in this reading
program and their SAT verbal score mean of 520 was compared to the national mean.
Discuss how this would require a One Sample t Test.
3. For the above example, how would you set up a two-tailed alternative hypothesis and what
would you conclude whether the null hypothesis was rejected?
4. How would you set up a one-tailed alternative hypothesis for the above example and what
would you conclude if the null hypothesis was rejected?
5. Assume that a One Sample t Test showed the following results: [t (49) = 4.21, p < .01].
Answer the following questions.
A. What is the probability that the null hypothesis is true?
B. What is the df of the study?
C. What is the n of the study?
D. What would you conclude?
Question for Discussion
6. Discuss a possible study topic that would require a One Sample t Test
Exercise for Chapter 25
Factual Questions
1. Which statistics should be reported before the results of a t test are reported?
2. Suppose you read this statement: “The difference between the means is statistically
significant at the .05 level (t = 2.333, df = 11).” Should you conclude that the null
hypothesis has been rejected?
3. Suppose you read this statement: “The null hypothesis was rejected (t = 2.810, df = 40,
p < .01).” Should you conclude that the difference is statistically significant?
4. Suppose you read this statement: “The null hypothesis was not rejected (t = –.926,
df = 24, p > .05).” Describe in words the meaning of the statistical term “p > .05.”
5. For the statement in Question 4, should you conclude that the difference is statistically
significant?
6. Suppose you read this statement: “For the difference between the means, t = 2.111 (df = 5,
n.s.).” Should you conclude that the null hypothesis has been rejected?
7. Which type of author seldom explicitly mentions the null hypothesis?
A. Authors of dissertations
B. Authors of journal articles
Exercise for Chapter 26
Factual Questions
1. ANOVA stands for what three words?
2. What is the name of the test that can be conducted with an ANOVA?
3. “An ANOVA can be appropriately used to test only the difference between two means.”
Is this statement “true” or “false”?
4. If the difference between a pair of means is tested with ANOVA, will the probability level
be different from that where the difference was tested with a t test?
5. Which statistic in an ANOVA table is of greatest interest to the typical consumer of
research?
6. Suppose you read this statement: “The difference between the means was not statistically
significant at the .05 level (F = 2.293, df = 12, 18).” Should you conclude that the null
hypothesis was rejected?
7. Suppose you read this statement: “The difference between the means was statistically
significant at the .01 level (F = 3.409, df = 14, 17).” Should you conclude that the null
hypothesis was rejected?
8. Suppose you saw this in the footnote to a One-Way ANOVA table: “p < .05.” Are the
differences statistically significant?
9. Suppose participants were classified according to their grade level in order to test the
differences among the means for the grade levels. Does this call for a “One-Way ANOVA”
or a “Two-Way ANOVA”?
10. Suppose that the participants were classified according to their grade levels and their country
of birth in order to study differences among means for both grade level and country of
birth. Does this call for a “One-Way ANOVA” or a “Two-Way ANOVA”?
Question for Discussion
11. Briefly describe a hypothetical study in which it would be appropriate to conduct a One-
Way ANOVA but not appropriate to conduct a t test
Exercise for Chapter 27
Factual Questions
(Assume there are equal numbers of participants in each cell)
Questions 1 through 3 below refer to this information: Two types of basketball instruction were
used with random samples of participants who either had previous experience of playing or did
not have previous experience. The means indicate the proficiency at playing basketball at the
end of treatment.
Type of instruction Row means
New Conventional
Previous experience M = 230.00 M = 200.00 M = 215.00
No previous experience M = 200.00 M = 230.00 M = 215.00
Column means M = 215.00 M = 215.00
1. Does there seem to be a main effect for type of instruction?
2. Does there seem to be a main effect for experience?
3. Does there seem to be an interaction?
Questions 4 through 6 below refer to this information: Random samples of participants with
back pain and headache pain were randomly assigned to two types of pain relievers. The means
below indicate the average amount of pain relief. A higher mean indicates greater pain relief.
Type of pain Row means
Back pain Headache
Type A pain reliever M = 25.00 M = 20.00 M = 22.50
Type B pain reliever M = 15.00 M = 10.00 M = 12.50
Column means M = 20.00 M = 15.00
4. Does there seem to be a main effect for type of pain (back pain versus headache pain)?
5. Does there seem to be a main effect for type of pain reliever?
6. Does there seem to be an interaction?
Questions 7 through 9 below refer to this ANOVA table:
Source F p
Age level (young, old) 13.25 .029
Region (north, south) 1.69 .321
Interaction (age region) 15.32 .043
7. Is the main effect for age level statistically significant at the .05 level?
8. Can the null hypothesis for the main effect of region be rejected at the .05 level?
9. Is the interaction between age and region statistically significant at the .05 level?
Question for Discussion
10. Briefly describe a hypothetical study in which it would be appropriate to conduct a two-
way ANOVA.
