Chapter 14—Hypothesis Tests Applied to
Means: Two Independent Samples
MULTIPLE CHOICE QUESTIONS
14.1+ The most important characteristic of two independent samples is
14.2+ Which of the following would most likely NOT be independent samples?
14.3 Which of the following would make you believe that you have two independent
groups?
14.4+ When testing the means of independent samples, the null hypothesis is best
thought of as
14.5 The distribution of differences between means is
14.6 The variance sum law deals with
Test Bank
14.7 When variables A and B are independent, the variance of A – B is equal to
14.8 The t statistic differs from z in that
14.9 Given the following equation, the only difference between this and our original
equation for z is:
2
2
2
1
2
1
21
21 )()(
NN
XX
z
+
−−−
=
14.10 To go from the equation in the previous problem to the equation for t we must
14.11+ When we speak about pooling variances we are referring to
14.12 We would NOT pool the variances if
14.13 The reason that we pool variances is to
Chapter 14
14.14 Our assumption that population variances are equal is called the assumption of
14.15+ A weighted average is
14.16 Which of the following formulae for t is correct?
14.17 When we have an independent sample t test, the degrees of freedom are equal to
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14.18+ The following data are taken from Chapter 14 and refer to a study of weight gain
in treated and untreated girls suffering from anorexia.
untreated
treated
Mean
-0.45
7.26
St Dev.
7.99
7.16
Variance
63.82
51.23
N
26
17
Which of the following formula for t in this situation would be a correct one?
14.19 In the previous example, how many df do we have?
14.20 In the anorexia example comparing Family Therapy and Control conditions the
null hypothesis would be
14.21+ If we reject the null hypothesis with a two-tailed test in the previous anorexia
condition, we would side with which of the following alternatives?
Chapter 14
14.22+ In the previous test on the treatment of anorexia, the resulting t was –3.22, which
was significant (p < .05). This tells us that
14.23 When we have very unequal sample variances, we should
14.24+ For a very conservative test when we don’t pool the variances we should
14.25 When we say that two independent variables, such as gender and age, are
confounded, we mean that
14.26 The normality assumptions behind the independent groups t test
14.27 One of our best aids in handling problems of non-normality is
Test Bank
14.28+ If we built on Doob and Gross’s study of horn-honking behavior to compare the
time it takes for people to honk at an older car versus the time to honk at an
expensive newer car, we could set it up as
14.29 An important reason for using random assignment in a study with independent
groups is to
14.30 In which of the following cases is it most useful to pool the variances?
14.31 Using the conservative test in which variances were not pooled that was described
in the text, on how many degrees of freedom would the t test on groups of 65 and
21 participants be based?
14.32+ A researcher was interested in examining the different levels of aggression shown
by college students and prisoners with life sentences. Aggression was measured
by surveys given during one session. Which analysis should the researcher
perform on the mean aggression scores of the groups?
14.33 What is the null hypothesis of the above example?
Chapter 14
14.34+ In deciding whether or not to pool the variances in calculating a t score, one
should consider
14.35 The null hypothesis of an independent samples t test is
14.36 In the example in the text assessing the effect of family therapy on anorexic girls
by the mean levels of weight gain, the difference between the independent
samples design used there and the related means design used in Chapter 13 is that
the independent samples design
14.37+ Mean scores in Tetris were recorded for both math majors and English majors.
The mean score for math majors was 20,752 (s12 = 851, N1 = 17) and the mean
score for English majors was 14,922 (s22 = 395, N2 = 56). The pooled variance
would probably be closest to which value?
d) 900
14.38 Which of the following is a reason why we may NOT find a significant difference
between two groups?
14.39 What statistical test is used for two independent groups?
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14.40 The statistical test that compares two or more means is a(n)
14.41 A chess team advisor wanted to examine how long it took his top two players,
Fishy Bobber and Chet Mate, to complete their moves. Over the course of 50
matches each, Fishy averaged 330 seconds to move while Chet averaged 420
seconds to move. If the overall standard deviation for Fishy and Chet was 45
seconds, what was the effect size of their difference?
14.42 We want to compare the scores of two different groups of people, those who are
high in authoritarianism versus those who are low in authoritarianism, on a scale
that measures leadership ability. What is the best statistical test to perform to see
if the two groups are different from each other on this measure?
14.43 The measure of the effect size for the difference between two groups is best seen
as
TRUE/FALSE QUESTIONS
populations with equal variances.
and a sample of 30, the df = 53.
samples t-tests.
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and women are perceiving his candidate. In his sample, political party
membership does not differ for males and females. Thus, gender and political
party are confounded.
independent variables is equal to the difference of their variances.
sample means cannot be compared with a t-test.
parents are two independent groups.
samples were drawn from populations that have means between 10 and 15.
OPEN-ENDED QUESTIONS
14.54 What is the two-tail critical value for an independent samples t-test (assuming
heterogeneity of variance) given the following samples sizes and p = .05?
a) N1 = 10; N2 = 10
b) N1 = 15; N2 = 10
c) N1 = 27; N2 = 25
14.55 A group of children exposed to violence on television (N = 20) scored higher on a
measure of aggression than a group of children who were not exposed to violence
on television (N = 22). t = 1.25. What can you conclude?
14.56 A researcher thinks that people who drive red cars drive faster than people who
drive white cars. He recorded the speed of a random sample of red and white cars
on a highway. The data follow.
Red Cars
White Cars
Mean
72.5 mph
69.75mph
Variance
7.32 mph
9.85 mph
Sample Size
53
49
a) What is the research hypothesis?
b) Is a one-tail or a two-tail test more appropriate?
c) Calculate t.
d) Is the research hypothesis supported? Explain?
14.57 Using the data from the previous example, what is the 95% confidence interval
for the true difference in speed?
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14.58 Calculate the pooled variance given the following information.
a) s12 = 26, N1 = 30 and s22 = 32, N2 = 40
b) s12 = 3.5, N1 = 12 and s22 = 4.6, N2 = 18
14.59 Indicate whether or not it would be appropriate to use pooled variances to
calculate t given the following information. Explain your answers.
a) s12 = 1.5, N1 = 30 and s22 = 8.5, N2 = 50
b) s12 = 10, N1 = 40 and s22 = 15, N2 = 48
14.60 Explain an appropriate method to compare means from independent samples
when the sample variances are heterogeneous.
14.61 Given the following data, calculate and interpret t.
Group
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
Score
12
13
14
15
15
18
19
20
22
23
1
2
3
5
7
10
11
14
32
14.62 Refer to the following output to answer these questions.
Group Statistics
181
19.49
5.78
.43
216
26.95
7.64
.52
GROUP
SUV
Sedan
Miles per Gallon
N
Mean
Std.
Deviation
Std. Error
Mean
Independent Samples Test
16.689
.000
-10.802
395
.000
-7.46
.69
-8.82
-6.10
-11.063
391.180
.000
-7.46
.67
-8.79
-6.14
Equal
variances
assumed
Equal
variances not
assumed
Miles per
Gallon
F
Sig.
Levene‘s Test for
Equality of
Variances
t
df
Sig.
(2-tailed)
Mean
Difference
Std. Error
Difference
Lower
Upper
95% Confidence
Interval of the
Difference
t–test for Equality of Means
a) Has the assumption of homogeneity of variance been met?
b) Which t-test should be used to interpret the data?
c) Write a sentence summarizing the results of the t-test.
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14.63 A movie critic believes people linger in the theatre after a movie for longer
periods following dramas than comedies. The data follow.
Dramas
Comedies
X
100 sec
90 sec
s2
35 sec
8 sec
N
50
150
a) What is the research hypothesis?
b) Is a one-tail or a two-tail test more appropriate?
c) Calculate t.
d) Is the research hypothesis supported? Explain
Answers to Open-ended Questions
Chapter 14.
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