School

University of California, Berkeley **We aren't endorsed by this school

Course

STAT 2

Subject

Statistics

Date

Sep 25, 2023

Type

Other

Pages

5

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Stat 2, Summer Session
Assignment 6
Name: ___________________________
Student ID: _______________________
Instructions:
YOU MUST SHOW ALL YOUR WORK TO RECEIVE FULL CREDIT.
You
will need a calculator and the normal table in the back of your textbook to do this
assignment. If the value you need is in between two values in the normal table, use the
one that is closest.
1. A student carries out a survey of UC Berkeley undergraduates by standing in a
heavily trafficked area near Sather Gate one Monday afternoon and asking
questions of the first 100 people who are willing to talk to him. Is this survey method
like taking a simple random sample of all UC Berkeley undergraduates? Explain why
or why not. If there is a potential for bias, name which types of bias you are most
concerned about, and explain why.
2. A researcher is interested in whether heavy marijuana use can increase the
likelihood of developing schizophrenia in young adults who have a family history of
schizophrenia. She starts her research by personally interviewing 100 young adults
with a family history of schizophrenia and asking them about how frequently they
use marijuana. Assuming that the 100 young adults she is interviewing are
representative of the population of young adults she is interested in, what other type
of bias might we be concerned about here? What kind of influence could this bias
have on her conclusions about the percent of young adults with a family history of
schizophrenia who smoke every day?
this
method
is
not
like
taking
a
simple
random
sample
because
it's
possible
that
there
is
selection
biasnon
response
or
a
comrence
sample
because
he's
only
asking
questions
to
students
who
are
willing
to
respond
also
it
might
bea
conveniencesample
because
he's
only
surveying
one
location
at
a
certain
time
and
day
these
are
a
concern
bis it
can
slow
the
survey
by
excluding
the
opinions
of
those
who
didn't
answer
or
were
not inthe
area
during
the
time
ofthe
survey
so
it'snot
representative
ofthe
population
as
a
random
sample
would
response
bias
ble
it's
likely
that
there
willbe
teenage
who
will
inaccurately
their
usage
this
bias
could
mate
the
percentage
smaller
therefore
affecting
the
common
between
the
heavy
marijuana
usage
and
schizophrenia

3. Several local universities hire a polling company to study how widespread cheating
is in online courses. For each of the challenges listed below that this company faces,
fill in the blank with the number matching the type of bias this challenge would make
us worry about the most. Each type of bias will be used exactly once.
(a) Students don't want to admit that they cheat and might lie about it. _________
(b) The company doesn't have contact information for all students. _________
(c) The survey the company will administer is optional. _________
Options:
1 - Selection bias
2 - Non-response bias
3 - Response bias
4. A polling company has been hired to estimate the percentage of people who use
Twitter among various demographic groups within the U.S. The polling company has
already surveyed one thousand people within the ages 18-44. This age group makes
up about 36.5% of the overall population of the U.S. Now the polling company wants
to survey people ages 45-64, who make up about 26.4% of the overall population of
the U.S. Other things being equal, about how many people should they survey in the
45-64 year old group to achieve a similar level of accuracy in their estimates in both
age groups?
Answer: _____________ people
Explain your answer in one sentence:
3
I
2
1000
we
need
to
survey
the
same
absolute
sample
size
bit
in
the
scenario
of a
big
survey
likethis
what
matters
is
the
actual
size
of the
sample
and
not
the
native
see
compared
tothe
population

5. In a company made up of 30,000 employees, 6,900 (23%) are enrolled in an
optional savings program. The company is considering changing the program and
decides to first take a poll of 500 randomly selected employees. In this problem we
will look at the
sample percentage
of employees who are enrolled in the program.
(a) Write down all elements of the box model.
(b) The average of the tickets in the box is _______ and the SD is _______.
(c) Consider the percentage of employees in the sample who are enrolled in the
program.
What is its expected value? __________%
What is its standard error? __________%
(d) Use the normal approximation to calculate the chance that the percentage of
employees in the sample who are enrolled in the program is between 22% and 24%.
Answer: _____________%
(e) How do you justify using the normal approximation in (d)? (Your answer should
include the name of a theorem and one or more numerical comparisons.)
23
1
77
o
soo
w
replacement
23
42
avg
2
0
23
SD
V1.23
771
42
23
i
m
t
number
in
pt
B
SD
ofbox
sample
size
100
loot
41.77
24 22
1
88
S3
1243331
53
22
24
g
Th
sa
sa
CLT
justifies normal
approximation
it
the
sample
size
is
large
enough
1.23111007
23
to
l
77
too
to
large
enoughsample
size