Statistics for the Behavioral Sciences by Frederick J. Gravetter, Larry B. Wallnau ISBN 10: 1305504917 ISBN 13: 9781305504912

620 CHAPTER 18 | The Binomial Test
The corresponding z-score (using Equation 18.2) is
z 5 X/n 2 p
Ïpq/n
0.72 2 0.60
5
Î 0.60s0.40d
5 0.12
0.0816 5 1.47
36
STEP 4
Make a decision about H 0
, and state a conclusion The obtained z-score is not in the
critical region. Therefore, we fail to reject the null hypothesis. On the basis of these data, you
conclude that the male/female proportions in the gender class are not significantly different
from the proportions in the psychology department as a whole.
PROBLEMS
1. Insurance companies charge young drivers more for
automobile insurance because they tend to have more
accidents than older drivers. To make this point,
an insurance representative first determines that
only 15% of licensed drivers are age 20 or younger.
Because this age group makes up only 15% of the
drivers, it is reasonable to predict that they should be
involved in only 15% of the accidents. In a random
sample of 80 accident reports, however, the representative
finds 26 accidents that involved drivers who
were 20 or younger. Is this sample sufficient to show
that younger drivers have significantly more accidents
than would be expected from the percentage of young
drivers? Use a two-tailed test with α = .05.
2. Güven, Elaimis, Binokay, and Tan (2003) studied
the distribution of paw preferences in rats using a
computerized food-reaching test. For a sample of
n = 144 rats, they found 104 right-handed animals.
Is this significantly more than would be expected if
right- and left-handed rats are equally common in the
population? Use a two-tailed test with α = .01.
3. In problem 9 in Chapter 17, we described a study
demonstrating that the color red is often associated
with male dominance. Hill and Barton (2005)
monitored the outcome of four combat sports (boxing,
Tae Kwon Do, Greco-Roman wrestling, and freestyle
wrestling) during the 2004 Olympic games and found
that participants wearing red outfits won significantly
more often than those wearing blue.
a. If athletes wearing red won 31 out of 50 matches,
is that sufficient to be significantly more than
would be expected by chance? Use a two-tailed
test with α = .05.
b. If 62 out of 100 wearing red won, is that enough to
be significant using a two-tailed test with α = .05.
c. Note that the percentage of winning for red
uniforms in part a is identical to the percentage in
part b (31/50 = 62/100 = 62%) however, one is
significant and the other is not. Explain why the
two samples lead to different conclusions.
4. Problems 5 and 6 in Chapter 17 cited a study showing
that people tend to choose partners who are similar to
themselves. Jones, Pelham, Carvallo, and Mirenberg,
(2004) demonstrated that people have a tendency to
select marriage partners with surnames that begin with
the same last letter as their own. The probability of
randomly matching two last names beginning with the
same letter is only p = 0.065 (6.5%).
a. If 19 out of 200 marriages involved brides and
grooms with last names beginning with the same
letter, is that enough to be significantly different
than would be expected by chance? Use a
two-tailed test with α = .05.
b. If 38 out of 400 marriages involved the same letter,
is that enough to be significant using a two-tailed
test with α = .05?
5. A researcher would like to determine whether people
really can tell the difference between bottled water
and tap water. Participants are asked to taste two
unlabeled glasses of water, one bottled and one tap,
and identify the one they think tastes better. Out of
40 people in the sample, 28 picked the bottled water.
Was the bottled water selected significantly more
often than would be expected by chance? Use a
two-tailed test with α = .05.
6. A recent survey of practicing psychotherapists
revealed that 25% of the individuals responding
agreed with the statement, “Hypnosis can be used
to recover accurate memories of past lives” (Yapko,
1994). A researcher would like to determine whether
this same level of belief exists in the general
population. A sample of 192 adults is surveyed and
65 believe that hypnosis can be used to recover
accurate memories of past lives. Based on these data,
can you conclude that beliefs held by the general
population are significantly different from beliefs
held by psychotherapists? Test with α = .05.
7. In 2005, Fung et al. published a study reporting that
patients prefer technical quality vs. interpersonal skills