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

264 CHAPTER 8 | Introduction to Hypothesis Testing
8. Childhood participation in sports, cultural groups,
and youth groups appears to be related to improved
self-esteem for adolescents (McGee, Williams,
Howden-Chapman, Martin, & Kawachi, 2006). In a
representative study, a sample of n = 100 adolescents
with a history of group participation is given a standardized
self-esteem questionnaire. For the general
population of adolescents, scores on this questionnaire
form a normal distribution with a mean of μ = 50 and
a standard deviation of σ = 15. The sample of groupparticipation
adolescents had an average of M = 53.8.
a. Does this sample provide enough evidence to conclude
that self-esteem scores for these adolescents
are significantly different from those of the general
population? Use a two-tailed test with α = .05.
b. Compute Cohen’s d to measure the size of the
difference.
c. Write a sentence describing the outcome of the
hypothesis test and the measure of effect size as it
would appear in a research report.
9. The psychology department is gradually changing its
curriculum by increasing the number of online course
offerings. To evaluate the effectiveness of this change,
a random sample of n = 36 students who registered
for Introductory Psychology is placed in the online
version of the course. At the end of the semester, all
students take the same final exam. The average score
for the sample is M = 76. For the general population
of students taking the traditional lecture class, the final
exam scores form a normal distribution with a mean
of μ = 71.
a. If the final exam scores for the population have
a standard deviation of σ = 12, does the sample
provide enough evidence to conclude that the new
online course is significantly different from the traditional
class? Use a two-tailed test with α = .05.
b. If the population standard deviation is σ = 18, is
the sample sufficient to demonstrate a significant
difference? Again, use a two-tailed test with
α = .05.
c. Comparing your answers for parts a and b, explain
how the magnitude of the standard deviation influences
the outcome of a hypothesis test.
10. A random sample is selected from a normal population
with a mean of μ = 30 and a standard deviation
of σ = 8. After a treatment is administered to the
individuals in the sample, the sample mean is found to
be M = 33.
a. If the sample consists of n = 16 scores, is the
sample mean sufficient to conclude that the treatment
has a significant effect? Use a two-tailed test
with α = .05.
b. If the sample consists of n = 64 scores, is the
sample mean sufficient to conclude that the
treatment has a significant effect? Use a two-tailed
test with α = .05.
c. Comparing your answers for parts a and b, explain
how the size of the sample influences the outcome
of a hypothesis test.
11. A random sample of n = 25 scores is selected from
a normal population with a mean of μ = 40. After
a treatment is administered to the individuals in the
sample, the sample mean is found to be M = 44.
a. If the population standard deviation is σ = 5, is the
sample mean sufficient to conclude that the treatment
has a significant effect? Use a two-tailed test
with α = .05.
b. If the population standard deviation is σ = 15, is
the sample mean sufficient to conclude that the
treatment has a significant effect? Use a two-tailed
test with α = .05.
c. Comparing your answers for parts a and b, explain
how the magnitude of the standard deviation influences
the outcome of a hypothesis test.
12. Brunt, Rhee, and Zhong (2008) surveyed 557 undergraduate
college students to examine their weight
status, health behaviors, and diet. Using body mass
index (BMI), they classified the students into four categories:
underweight, healthy weight, overweight, and
obese. They also measured dietary variety by counting
the number of different foods each student ate from
several food groups. Note that the researchers are not
measuring the amount of food eaten, but rather the
number of different foods eaten (variety, not quantity).
Nonetheless, it was somewhat surprising that the four
the four weight groups all ate essentially the same
number of fatty and/or sugary snacks.
Suppose a researcher conducting a follow up study
obtains a sample of n = 25 students classified as
healthy weight and a sample of n = 36 students classified
as overweight. Each student completes the food
variety questionnaire, and the healthy-weight group
produces a mean of M = 4.01 for the fatty, sugary
snack category compared to a mean of M = 4.48 for
the overweight group. The results from the Brunt,
Rhee, and Zhong study showed an overall mean
score of μ = 4.22 for the sweets or fats food group.
Assume that the distribution of scores is approximately
normal with a standard deviation of σ = 0.60.
a. Does the sample of n = 36 indicate that number of
fatty, sugary snacks eaten by overweight students
is significantly different from the overall population
mean? Use a two-tailed test with α = .05.
b. Based on the sample of n = 25 healthy-weight
students, can you conclude that healthy-weight
students eat significantly fewer fatty, sugary snacks
than the overall population? Use a one-tailed test
with α = .05.