. An educational psychologist would like to determine whether access to computers
has an effect on grades for high school students. One group of n = 16 students has
home room each day in a computer classroom in which each student has a computer. A compari
1. a. The pooled variance is 72, the standard error is 3, and t = 1.17. With a critical value
of t = 2.042, fail to reject the null hypothesis.
b. Cohen's d = 3.5A172 = 0.412
c. The results show no significant difference in grades for students with comput
2. A researcher report states that there is a significant difference between treatments
for an independent-measures design with t(28) = 2.27.
a. How many individuals participated in the research study? (Hint: Start with the
dfvalue.)
b. Should the report
2. a. The df = 28, so the total number of participants is 30.
b. A significant result is indicated by p < .05.
Three assumptions that should be satisfied before you use the independentmeasures t formula for hypothesis testing:
1. The observations within each sample must be independent (see p. 254).
2. The two populations from which the samples are selected must be normal.
3. The two populations from which the samples are selected must have equal
variances.
1. A researcher is using an independent-measures design to evaluate the difference
between two treatment conditions with n = 8 in each treatment. The first treatment produces M = 63 with a variance of s2 = 18, and the second treatment has
M = 58 with s2 =
1. a. The pooled variance is 16, the estimated standard error is 2, and t(14) = 2.50. With a
one-tailed critical value of 1.761, reject the null hypothesis. Scores in the first treatment are
significantly higher than scores in the second.
b. Increasing th
2. The homogeneity of variance assumption requires that the two sample variances
be equal. (True or false?)
2. False. The assumption is that the two population variances are equal.
3. When you are using an F-max test to evaluate the homogeneity of variance
assumption, you usually do not want to find a significant difference between the
variances. (True or false?)
3. True. If there is a significant difference between the two variances, you cannot do the t test
with pooled variance
1. Describe the basic characteristics of an independent
measures, or a between-subjects, research study.
1. An independent-measures study uses a separate sample for each of the treatments or populations being compared.
2. Describe what is measured by the estimated standard
error in the bottom of the independent-measures
t statistic
2. The standard error for the independent measures t provides an estimate of the standard distance between a sample mean difference (M1 - M2) and the population mean difference (?1 - ?2). When the two samples come from populations with the same mean (when
3. If other factors are held constant, explain how
each of the following influences the value of the
independent-measures t statistic and the likelihood
of rejecting the null hypothesis:
a. Increasing the number of scores in each sample.
b. Increasing the
3. a. The size of the two samples influences the magnitude of the estimated standard error in
the denominator of the t statistic. As sample size increases, the value of t also increases
(moves farther from zero), and the likelihood of rejecting H0 also in
4. Describe the homogeneity of variance assumption
and explain why it is important for the independentmeasures t test
4. The homogeneity of variance assumption specifies that the variances are equal for the two populations from which the samples are obtained. If this assumption is violated, the t statistic can cause misleading conclusions for a hypothesis test.
5. One sample has SS = 48 and a second sample has
SS = 32.
a. If n = 5 for both samples, find each of the sample
variances and compute the pooled variance.
Because the samples are the same size, you should
find that the pooled variance is exactly halfway
5. a. The first sample has s2 = 12 and the second has s2 = 8. The pooled variance is 80/8 = 10 (halfway between).
b. The first sample has s2 = 12 and the second has s2 = 4. The pooled variance is 80/12 = 6.67 (closer to the variance for the larger sample)
6. One sample has SS = 70 and a second sample has
SS = 42.
a. Ifn = 8 for both samples, find each of the sample
variances, and calculate the pooled variance.
Because the samples are the same size, you should
find that the pooled variance is exactly halfwa
6. a. The first sample has a variance of 10, the second sample variance is 6, and the pooled variance is 8 (halfway between).
b. The first sample has a variance of 10, the second sample variance is 14, and the pooled variance is 112/10 = 11.2 (closer to t
7. As noted on page 320, when the two population means
are equal, the estimated standard error for the
independent-measures t test provides a measure of
how much difference to expect between two sample
means. For each of the following situations, assume
t
7. a. The pooled variance is 6 and the estimated standard error is 1.50.
b. The pooled variance is 24 and the estimated standard error is 3.
c. Larger variability produces a larger standard error.
8. Two separate samples, each with n = 12 individuals,
receive two different treatments. After treatment, the first
sample has SS = 1740 and the second has SS = 1560.
a. Find the pooled variance for the two samples.
b. Compute the estimated standard error
8. a. The pooled variance is 150.
b. The estimated standard error is 5.00.
c. A mean difference of 8 would produce t = 8/5 = 1.60. With df = 22 the critical values are �2.074. Fail to reject H0.
d. A mean difference of 12 would produce t = 12/5 = 2.40. Wi
9. Two separate samples receive two different treatments.
The first sample has n = 9 with SS = 710, and the
second has n = 6 with SS = 460.
a. Compute the pooled variance for the two samples.
b. Calculate the estimated standard error for the
sample mean d
9. a. The pooled variance is 90.
b. The estimated standard error is 5.
c. A mean difference of 10 points produces t = 2.00. With critical boundaries of �2.160, fail to reject H0
d. A mean difference of 13 points produces t = 2.60. With critical boundaries
10. For each of the following, assume that the two
samples are selected from populations with equal
means and calculate how much difference should be
expected, on average, between the two sample means.
a. Each sample has n = 5 scores with s2 = 38 for the
10. a. The estimated standard error for the sample mean difference is 4 points.
b. The estimated standard error for the sample mean difference is 2 points.
c. Larger samples produce a smaller standard error.
11. For each of the following, calculate the pooled
variance and the estimated standard error for the
sample mean difference
a. The first sample has n = 4 scores and a variance of
s2 = 55, and the second sample has n = 6 scores
and a variance of s2 = 63.
11. a. The pooled variance is 60 and the estimated standard error is 5.
b. The pooled variance is 240 and the estimated standard error is 10.
c. Increasing the sample variance produces an increase in the standard error.
12. A researcher conducts an independent-measures study
comparing two treatments and reports the t statistic as
t(30) = 2.085.
a. How many individuals participated in the entire study
b. Using a two-tailed test with a = .05, is there a
significant differe
12. a. The two samples combined have a total of 32 participants.
b. With df = 30 and ? = .05, the critical region consists of t values beyond 2.042. The t statistic is in the critical region. Reject H0 and conclude that there is a significant difference.
13. Hallam, Price, and Katsarou (2002) investigated the
influence of background noise on classroom
performance for children aged 10 to 12. In one part of
the study, calming music led to better performance on
an arithmetic task compared to a no-music condi
13. a. Using df = 30, , because 34 is not listed in the table, and ? = .05, the critical region
consists of t values beyond 2.042. The pooled variance is 81, the estimated standard
error is 3, and t(34) = 7.6/3 = 2.53. The t statistic is in the critical r
14. Do you view a chocolate bar as delicious or as
fattening? Your attitude may depend on your gender.
In a study of American college students, Rozin, Bauer,
and Catanese (2003) examined the importance of food
as a source of pleasure versus concerns about
14. a. The pooled variance is 90, the estimated standard error is 4, and t = 9/4 = 2.25. With
df = 22 the critical value is 2.074. Reject the null hypothesis and conclude that there is a
significant difference in attitude between males and females.
b. r2
15. In a study examining overweight and obese college
football players, Mathews and Wagner (2008) found
that on average both offensive and defensive linemen
exceeded the at-risk criterion for body mass index
(BMI). BMI is a ratio of body weight to height
15. a. For the offensive linemen, the standard error is 0.97 and t = 4.54. For a one-tailed test
with df = 16, the critical value is 2.583. Reject the null hypothesis. The offensive
linemen are significantly above the criterion for BMI.
b. For the defensi
16. Functional foods are those containing nutritional
supplements in addition to natural nutrients. Examples
include orange juice with calcium and eggs with
omega-3. Kolodinsky, et al. (2008) examined attitudes
toward functional foods for college students
16. a. The pooled variance is 0.24, the estimated standard error is 0.22, and t = 1.18. For a
two-tailed test with df = 18 the critical value is 2.101. Fail to reject the null hypothesis.
There is no significant difference between the two groups.
b. For t
17. In 1974, Loftus and Palmer conducted a classic study
demonstrating how the language used to ask a question
can influence eyewitness memory. In the study,
college students watched a film of an automobile
accident and then were asked questions about wha
17. a. The research prediction is that participants who hear the verb "smashed into" will
estimate higher speeds than those who hear the verb "hit." For these data, the pooled variance is 33, the estimated standard error is 2.10, and t(28) = 3.24. With df
18. Numerous studies have found that males report higher
self-esteem than females, especially for adolescents
(Kling, Hyde, Showers, & Buswell, 1999). Typical
results show a mean self-esteem score ofM = 39.0 with
SS = 60.2 for a sample ofn = 10 male adole
18. a. The pooled variance is 7.2, the estimated standard error is 1.2, and t(18) = 3.00. For a
one-tailed test with df = 18 the critical value is 2.552. Reject the null hypothesis.
There is a significant difference between the two groups.
b. For 95% conf
19. A researcher is comparing the effectiveness of two sets
of instructions for assembling a child's bike. A sample
of eight fathers is obtained. Half of the fathers are
given one set of instructions and the other half
receives the second set. The researc
19. a. The null hypothesis states that there is no difference between the two sets of instructions, H0: ?1 - ?2 = 0. With df = 6 and ? = .05, the critical region consists of t values beyond �2.447. For the first set, M = 6 and SS = 16. For the second set,
20. When people learn a new task, their performance
usually improves when they are tested the next day,
but only if they get at least 6 hours of sleep (Stickgold,
Whidbee, Schirmer, Patel, & Hobson, 2000). The
following data demonstrate this phenomenon. T
20. The pooled variance is 63, the estimated standard error is 3.00, and t = 7/3 = 2.33. With df = 26 the critical value is 2.056. Reject the null hypothesis and conclude that there is a significant difference between the two sleep conditions.
21. Steven Schmidt (1994) conducted a series of
experiments examining the effects of humor on
memory. In one study, participants were given a mix
of humorous and nonhumorous sentences and
significantly more humorous sentences were recalled.
However, Schmi
21. The humorous sentences produced a mean of M = 4.25 with SS = 35, and the non-
humorous sentences had M = 4.00 with SS = 26. The pooled variance is 2.03, the
estimated standard error is 0.504, and t = 0.496. With df = 30, the critical value is 2.042.
F
22. Downs and Abwender (2002) evaluated soccer players
and swimmers to determine whether the routine blows
to the head experienced by soccer players produced
long-term neurological deficits. In the study,
neurological tests were administered to mature soc
22. a. The null hypothesis states that the type of sport does not affect neurological performance. For a one-tailed test, the critical boundary is t = 1.796. For the swimmers, M = 9 and SS = 44. For the soccer players, M = 6 and SS = 24. The pooled varian
23. Research has shown that people are more likely
to show dishonest and self-interested behaviors
in darkness than in a well-lit environment
(Zhong, Bohns, & Gino, 2010). In one experiment,
participants were given a set of 20 puzzles and
were paid $0.50
23. a. The null hypothesis states that the lighting in the room does not affect behavior. For the
well-lit room the mean is M = 7.55 with SS = 42.22. For the dimly-lit room, M = 11.33
with SS = 38. The pooled variance is 5.01, the standard error is 1.06,
What's the difference between between subject design and repeated measures design?
Between subject design is the study of two different groups while repeated measures research/within subject design is two sets of data which is taken from the same group of participants
If H0 is U1-U2=0 and the confidence interval is 3.798 to 12.202 and 0 is concluded as accepted in the confidence interval then it is the same saying __________
failure to reject H0
standard error and it's relationship to sample varience and sample size
(a) (Increase) Sample varience
(a) (Increase) standard error (increase) Sample error
(b) (Increase) sample size (decrease) Sample errorq
3 Assumptions of an independent t-test
(1) Observation of each sample must be independent
(2) The two populations from which the sample is selected must be normal
(3) The population from which the samples are selected must have equal variances "homogenize of variance
homogenize of variance
The population from which the samples are selected must have equal variances
What does Hartey's F-Max test do?
This test tries to get an understanding of how different the sample variances are. If it fails to reject H0 then it is good news because the differences are not extreme enough to be a problem