The scores of a random sample of 8 students on a physics
test are as follows: 60, 62, 67, 69, 70, 72, 75, and 78.

Test
to see if the sample mean is significantly different from
65 at the .05 level. Report the t and p values.

The researcher
realizes that she accidentally recorded the score
that should have been 76 as 67. Are these corrected scores
significantly different from 65 at the .05 level? (relevant
section)

A (hypothetical) experiment is conducted on the effect of
alcohol on perceptual motor ability. Ten subjects are each
tested twice, once after having two drinks and once after having
two glasses of water. The two tests were on two different days
to give the alcohol a chance to wear off. Half of the subjects
were given alcohol first and half were given water first. The
scores of the 10 subjects are shown below. The first number
for each subject is their performance in the "water" condition.
Higher scores reflect better performance. Test to see if alcohol
had a significant effect. Report the t and p values. (relevant section)

water

alcohol

16

13

15

13

11

10

20

18

19

17

14

11

13

10

15

15

14

11

16

16

The scores on a (hypothetical) vocabulary
test of a group of 20 year olds and a group of 60 year olds
are shown below.

20 yr olds

60 yr olds

27

26

26

29

21

29

24

29

15

27

18

16

17

20

12

27

13

Test the mean difference for significance
using the .05 level. (relevant
section).

List
the assumptions made in computing your answer.(relevant section)

The sampling distribution of a statistic is normally distributed
with an estimated standard error of 12 (df = 20). (a) What
is the probability that you would have gotten a mean of 107
(or more extreme) if the population parameter were 100? Is
this probability significant at the .05 level (two-tailed)?
(b) What is the probability that you would have gotten a mean
of 95 or less (one-tailed)? Is this probability significant
at the .05 level? You may want to use the t
Distribution calculator for this problem. (relevant
section)

How do you decide whether to use an independent
groups t test or a correlated t test (test of dependent means)?
relevant section & (relevant section)

An
experiment compared the ability of three groups of subjects
to remember briefly-presented chess positions. The data are
shown below.

Non-players

Beginners

Tournament players

22.1

32.5

40.1

22.3

37.1

45.6

26.2

39.1

51.2

29.6

40.5

56.4

31.7

45.5

58.1

33.5

51.3

71.1

38.9

52.6

74.9

39.7

55.7

75.9

43.2

55.9

80.3

43.2

57.7

85.3

a. Using the Tukey HSD procedure, determine which
groups are significantly different from each other at the
.05 level. (relevant section)

b. Now compare each pair of groups using
t-tests. Make sure to control for the familywise error rate
(at 0.05) by using the Bonferroni correction. Specify the
alpha level you used.

Below are data showing the results of six subjects on a memory
test. The three scores per subject are their scores on three
trials (a, b, and c) of a memory task. Are the subjects getting
better each trial? Test the linear effect of trial for the
data.

a

b

c

4

6

7

3

7

8

2

8

5

1

4

7

4

6

9

2

4

2

a. Compute L for
each subject using the contrast weights -1, 0, and 1. That
is, compute (-1)(a) + (0)(b) + (1)(c) for each subject.

b. Compute a one-sample t-test on this
column (with the L values for each subject) you created. (relevant
section)

Participants threw darts at a target. In one condition,
they used their preferred hand; in the other condition,
they used their other hand. All subjects performed in both
conditions (the order of conditions was counterbalanced).
Their scores are shown below.

Preferred

Non-preferred

12

7

7

9

11

8

13

10

10

9

Which kind of t-test should
be used?

Calculate
the two-tailed t and p values using this t test.

Calculate
the one-tailed t and p values using this t test.

Assume the data in the previous problem were collected
using two different groups of subjects: One group used their
preferred hand and the other group used their non-preferred
hand. Analyze the data and compare the results to those for
the previous problem (relevant
section)

You have 4 means, and you want to compare
each mean to every other mean. (a) How many
tests total are you going to compute? (b) What would
be the chance of making at least one Type I
error if the Type I error for each test was .05 and the
tests were independent? (relevant
section & relevant
section ) (c) Are the tests independent and
how does independence/non-independence affect the
probability in (b).

In an experiment, participants
were divided into 4 groups. There were 20 participants
in each group, so the degrees of freedom (error)
for this study was 80 - 4 = 76. Tukey's HSD
test was performed on the data. (a) Calculate
the p value for each pair based on the Q value
given below. You will want to use the Studentized
Range Calculator. (b) Which differences are significant
at the .05 level? (relevant
section

Comparison of Groups

Q

A - B

3.4

A - C

3.8

A - D

4.3

B - C

1.7

B - D

3.9

C - D

3.7

If you have 5 groups in your study, why shouldn't you
just compute a t test of each group mean with each other
group mean? (relevant
section)

You are conducting a study to see if
students do better when they study all at once or in intervals.
One group of 12 participants took a test after studying
for one hour continuously. The other group of 12 participants
took a test after studying for three twenty minute sessions.
The first group had a mean score of 75 and a variance
of 120. The second group had a mean score of 86 and a
variance of 100.

What is the
calculated t value? Are the mean test scores of these
two groups significantly different at the .05 level?

What
would the t value be if there were only 6 participants
in each group? Would the scores be significant at the
.05 level?

A new test was designed to have
a mean of 80 and a standard deviation of 10. A random sample
of 20 students at your school take the test, and the mean
score turns out to be 85. Does this score differ significantly
from 80? To answer this
problem, you may want to use the Normal
Distribution Calculator.(relevant
section)

You perform a one-sample t test and calculate
a t statistic of 3.0. The mean of your sample was 1.3 and
the standard deviation was 2.6. How many participants were
used in this study? (relevant section)

True/false:
The contrasts (-3, 1 1 1) and (0, 0 , -1, 1) are orthogonal.
(relevant section)

True/false:
If you are making 4 comparisons between means, then based
on the Bonferroni correction, you should use an alpha level
of .01 for each test. (relevant section)

True/false:
Correlated t tests almost always have greater power than
independent t tests. (relevant section)

True/false:The graph below represents a violation of the
homogeneity of variance assumption. relevant section)

True/false: When you are conducting a one-sample t test
and you know the population standard deviation, you look
up the critical t value in the table based on the degrees
of freedom. (relevant section)

Questions from Case Studies:

The following questions use data from the Angry Moods (AM) case study.

(AM#17) Do athletes or non-athletes calm down more
when angry? Conduct a t test to see if the difference
between groups in Control-In scores is statistically
significant.

Do people in general have a higher Anger-Out
or Anger-In score? Conduct a t test on the difference
between means of these two scores. Are these two means
independent or dependent? (relevant section)

Compare each mean to the
neutral mean. Be sure to control for
the familywise error rate. (relevant section)

Does a "felt smile" lead to more leniency
than other types of smiles? (a)
Calculate L (the linear combination) using the following
contrast weights false: -1, felt: 2, miserable: -1,
neutral: 0. (b) Perform a significance test on this
value of L. (relevant section)

The following questions are from the Animal Research (AR) case study.

(AR#8) Conduct an independent samples t
test comparing males to females on the belief that
animal research is necessary. relevant section)

(AR#9) Based on the t test you
conducted in the previous problem, are
you able to reject the null hypothesis
if alpha = 0.05? What about if alpha
= 0.1? relevant section)

(AR#10) Is there any evidence that the
t test assumption of homogeneity of variance is violated
in the t test you computed in #25? relevant section)

The following questions use data from the ADHD Treatment (AT) case study.

Compare each dosage with the dosage below it (compare
d0 and d15, d15 and d30, and d30 and d60). Remember that
the patients completed the task after every dosage. (a)
If the familywise error rate is .05, what is the alpha
level you will use for each comparison when doing the Bonferroni
correction? (b) Which differences are significant at this
level? (relevant section)

Does performance increase
linearly with dosage?

Plot
a line graph of this data.

Compute
L for each patient. To
do this, create a new
variable where you multiply
the following coefficients
by their corresponding
dosages and then sum up
the total: (-3)d0 + (-1)d15
+ (1)d30 + (3)d60 (see
#8). What is the mean of
L?

Perform a significance
test on L. Compute the 95% confidence interval for L.
(relevant
section)