Name__________PSU ID.docx

Name________________________________
PSU ID_____________________________
STAT 100 Lesson 13 Assignment
Answer the following questions and submit for grading. Each
question or part of a question is worth 1 point except: 1, 2A,
2B, 2C, 3E, 4E, 5D, & 6C are worth 2 points; 7- 7 is worth 6
points.
1.
An ESP experiment is done in which a participant guesses
which of 8 cards the researcher has randomly picked, where
each card is equally likely to be selected. This is repeated for
200 trials. The null hypothesis is that the subject is guessing,
while the alternative is that the subject has ESP and can guess
at higher than the chance rate. Write out the type 1 and type 2
errors in terms of this problem.
2.
For each of the following, write out the null and alternative
hypotheses. Also identify what type of data is found. Refer to
the information inTable 13.1.
a.
Do female students, on the average, have a higher GPA?
b.
Is there a linear relationship between height and weight?
c.
Is there a difference in the proportions of male and female
college students who smoke?
3.
A Researcher asked a sample of 50 1st grade teachers and a

sample of 50 12th grade teachers how much of their own money
they spent on school supplies in the previous school year. The
researcher wanted to see if the mean spending at one grade level
is different from the mean spending at another grade level.
Two-sample T for 1st_Grade vs 12th_Grade
N Mean StDev SE Mean
1st_Grade 50 111.2 88.9 13
12th_Grade 50 49.5 38.8 5.5
Difference = mu 1st_Grade - mu 12th_Grade
Estimate for difference: 61.7
95% CI for difference: (34.3, 89.1)
T-Test of difference = 0 (vs not =): T-Value = 4.50 P-Value =
0.000 DF = 66
Figure A.1.
a.
What is the response variable in this problem?
b.
What is the explanatory variable in this problem?
c.
What type of variable is the response variable? categorical or
measurement
d.
What is the appropriate population value for this problem?

population mean or population proportion
e.
Write out the null and alternative hypotheses in terms of the
appropriate population value.
f.
On the output in Figure A.1 the test statistic is 4.50. Use this
test statistic to write a one-sentence interpretation of the p-
value in terms of this problem.
g.
What conclusion can be made in terms of this problem? Why?
h.
Using the 95% confidence interval of the difference as your
basis, do you think practical significance has been found with
regard to the mean amount spent when comparing 1st grade
teachers to 12th grade teachers? Include reasoning. Hint: Refer
to Example 13.10.
4.
A survey asked 2000 people whether or not they frequently
exceed the speed limit. The collected data is summarized in the
following contingency table. The goal is to determine if there is
a difference in the population proportion that say “yes” when
comparing those who are under 40 years in age to those who are
at least 40 years in age.
Table A.1. Data Summary
Frequently Exceed the Speed Limit?
Age
Yes

No
TotalAge under 40
600 (60%)
400
1000
Age 40 and above
450 (45%)
550
1000
Total
1050
950
2000
a.
b.
What is the explanatory variable in this problem?
c.
measurement
d.
e.
f.
On the output found in Figure A.2 the test statistic is 6.72. Use
this test statistic to write out a one-sentence interpretation of
the p-value in terms of this problem.

g.
h.
Compare the sample percent (proportion) that said yes for the
two age groups that are found in Table A.1. Do you believe the
results are practically significant? Include reasoning.
i.
Could a Chi-square Test also be used to analyze this data?
Why? (Hint: Refer back to lesson assignments in Lesson 7.)
Test and CI for Two Proportions
Sample XN Sample p
< 40 yrs 600 1000 0.60
≥ 40 yrs 450 1000 0.45
Estimate for p(1) - p(2): 0.15
95% CI for p(1) - p(2): (0.107, 0.193)
Test for p(1) - p(2) = 0 (vs not = 0): Z = 6.72 P-Value = 0.000
Figure A.2.
5.
For patients with a particular disease, the population proportion
of those successfully treated with a standard treatment that has
been used for many years is .75. A medical research group
invents a new treatment that they believe will be more
successful, i.e., population proportion will exceed .75. A doctor
plans a clinical trial he hopes will prove this claim. A sample of
100 patients with the disease is obtained. Each person is treated
with the new treatment and eventually classified as having

either been successfully or not successfully treated with the new
treatment.
a.
b.
measurement
c.
d.
e.
Find the test statistic on the output found below. Use this test
statistic to write a one-sentence interpretation of the p-value in
terms of this problem.
f.
Test and CI for One Proportion
Test of p = 0.75 vs p > 0.75
Sample X N Sample p Z-Value P-Value
1 80 100 0.800000 1.15 0.124
Figure A.3.
6. Refer to the information found in the article entitled 21st

Birthday from the Penn State Pulse (January, 2001). This was
previously used in Lesson 9.
a.
What is the majority of the type of data summarized on the first
page of this article? Measurement or categorical
b.
What population value should be used with this data?
c.
At the bottom of the first page of the article you find the
statement “* statistically significant at the .05 level.” This
statement implies that the p-value is ≤ .05. Find the “*”s on the
first page of the article. Precisely what two results are
statistically significant? State these results in terms of the
appropriate population value (ie: population mean or population
proportion).
Source: Penn State Pulse, 21st Birthday, January 2001
7. Refer to the following article located in the Library Reserves-
-use the Library Reserves link in Angel
Source: Kirchheimer, S. (May 17, 2003). Secondhand Smoke
Study Raises Ire
Answer the following questions about the article.
Question 1:
In studies that compare never smokers married to smokers with
never smokers married to never smokers, the explanatory
variable is ______
a.
whether or not the spouse smokes.

b.
whether or not the person was married.
c.
whether or not the person developed lung cancer.
d.
whether or not the smoke is secondhand.
Question 2:
A study that compares never smokers married to smokers with
never smokers married to never smokers is which of the
following?
a.
randomized experiment
b.
observational study
c.
matched pairs study
Question 3:
The number 30% in this article represents which of the
following quantities?
a.
risk
b.
relative risk
c.
increased risk

d.
odds
Question 4:
Enstrom’s study is which of the following?
a.
b.
prospective study
c.
retrospective study
Question 5:
This article identifies the funding source used by Enstrom. As a
statistical sleuth, what should you conclude from Enstrom’s
study after knowing his funding source?
a.
results are definitely biased
b.
must first evaluate scientific procedures used in study before
interpreting results
c.
results are definitely unbiased
Question 6:
Which of the following is not a concern about the study that
was conducted by Enstrom?
a.
extending conclusions to all people in the United States

b.
the existence of confounding variables
c.
smoking habits probably changed from 1972 to 1998
d.
results are based on a very small sample size
Question 7:
Now apply the seven critical components that are found in
Chapter 2 of your textbook to this article. List out each
component and provide a comment about each component based
on what you have discovered when reading the article. If the
article does not provide sufficient information about a certain
component, just provide a plausible explanation and/or
suggestion.
Please submit this assignment.
6
Name________________________________
PSU ID_____________________________
STAT 100 Lesson 12 Assignment
Answer the following questions and submit for grading. Each
question or part of a question is worth 1 point.
1.
Researchers asked a sample of 50 1st grade teachers and a
sample of 50 12th grade teachers how much of their own money
they spent on school supplies in the previous school year. They
wanted to see if teachers at one grade level spend more than

teachers at the other grade level.
a.
What type of study is found—observational or randomized
experiment? Explain.
b.
What is the experimental or observational unit?
c.
What is the response variable?
d.
What is the explanatory variable?
e.
Do we have to worry about confounding variables in this
instance? Why? If so identify a possible confounding variable?
f.
Are either of the terms retrospective study or prospective study
relevant? Explain.
2.
A research team compared two methods of measuring tread wear
on tires. Eleven tires were each measured for tread wear by two
different methods: one method was based on weight while the
other method was based on groove wear. For convenience, each
tire was measured first by weight method and then second by
the groove wear.
a.
The two samples are which of the following: two independent or
two dependent (matched pairs)? Explain.
b.

c.
d.
e.
3.
A study wants to determine if taking fish oils can reduce
depressive symptoms. A group of 50 volunteers who suffered
from mild depression were randomly divided into two groups.
Each person was given a three-month’s supply of capsules. One
group was given capsules that contained fish oils while the
other group was given capsules that look and tasted like fish
oils, but actually only contained sugar. Neither the participants
nor the investigator knew what type of capsule they were
taking. At the end of the month, a psychologist evaluated them
to determine if their depressive symptoms had changed.
Therefore, we are comparing the “change in depressive
symptoms” for individuals in two groups. Explain whether
each of the following terms applies to this study.
a.
observational study
b.
c.
placebo

d.
placebo effect
e.
single-blind
f.
double-blind
g.
matched pairs (dependent samples)
h.
block design
i.
independent samples
j.
explanatory variable (What is it?)
k.
response variable (What is it?)
4.
Does the use of cell phones lead to a higher incidence of brain
cancer? People with brain cancer were matched with people who
did not have brain cancer on age, gender, and living
environment. Each participant in the study was asked to answer
questions about previous life experiences and exposures.
Determine whether or not each of the following terms applies to
this observational study.
a.
prospective

b.
retrospective
c.
case-control study
5.
A study involving ten people wants to compare the effectiveness
of two different brands of antihistamines with regard to
enhancing sleep. Each person is randomly assigned to take
Antihistamine A on one night and Antihistamine B on the other
night. With each person, the hours of sleep were recorded for
each night. Explain whether each of the following terms applies
to this study.
a.
observational study
b.
c.
carry-over effect (confounding)
d.
matched pairs (dependent samples)
e.
explanatory variable (What is it?)
f.
response variable (What is it?)
6.
Suppose the study found in the previous problem instead found
that each person took Antihistamine A on the first night and

Antihistamine B on the second night. What terms that did not
apply to the previous problem now apply to this problem?
Explain.
7.
Are you annoyed with spam e-mail? Suppose a random sample
of 200 Penn State students was asked this question of which
80% said that they are annoyed. From the provided information
we can find the following:
sample percent = 80% (sample proportion = .80)
standard deviation (S.D.) = .03
a.
Set up the calculation of a 95% confidence interval to estimate
the population proportion of Penn State students who are
annoyed by spam e-mail? (Hint: refer to Example 12.5)
b.
Knowing that the margin of error = .06 or 6%, write out a one-
sentence interpretation of the margin of error.
c.
The 95% confidence interval to estimate the population
proportion of Penn State students who are annoyed by spam e-
mail is (.74 to .86). Write out a one-sentence interpretation of
this confidence interval.
d.
What type of data is used in this example—categorical or
measurement?
e.
What would happen to the size of the margin of error or
confidence interval if the level of confidence were instead

99.7%? Explain.
8.
Explain what will happen to the width of a confidence interval
(increase, decrease, or remain the same) as a result of each of
the following changes:
a.
Population size is doubled from 5 million to 10 million
b.
Confidence level lowered from 98% to 90%
c.
Sample size is doubled from 500 to 1000
9.
A sample of 200 students in a Stat class were asked “How long
did you sleep last night?” The results are found below.
sample mean = 6.4 hours
S.D. = 1.6 hours
standard error (S.E.) = .11 hours
sample size (n) = 200
a.
Set up the calculation of a 95% confidence interval to estimate
the population mean number of hours slept last night.
b.
Knowing that the margin of error = .22, write out a one-
sentence interpretation of the margin of error.

c.
The 95% confidence interval to estimate the population mean
number of hours slept last night is (6.18 to 6.62) hours. Write
out a one-sentence interpretation of this confidence interval.
d.
What type of data is used in this example?
e.
What would happen to the size of the margin of error or
confidence interval if the level of confidence were instead 68%?
Explain
10.
A 95% confidence interval for the proportion of women that
have ever dozed off while driving is 0.07 to 0.14. For men, a
95% confidence interval for the proportion that have ever dozed
off while driving is 0.19 to 0.25. Assume both intervals were
computed using large random samples.
a.
What conclusion can be made about the two population
proportions that have dozed off while driving? Why?
b.
Rewrite each confidence interval in terms of percents rather
than proportions. Does the conclusion remain the same?
Explain.
c.
two dependent (matched pairs)?
d.
What type of data is found in this problem—categorical or
measurement?

e.
Would the conclusion remain the same if the two confidence
intervals had instead been calculated at 90% confidence?
Explain.
11.
Attention Deficient Hyperactivity Disorder (ADHD)is a
diagnosis applied to children who exhibit the following
behaviors: (1) inattention (2) impulsiveness, (3) hyperactivity.
ADHD is now known to be a lifelong problem where
adolescents and adults continue to exhibit symptoms.
Researchers at the University of Wisconsin (Heiligenstein E. et
al., 1999) explored both psychological and academic
functioning in ADHD college students. Theyreviewed charts of
students who voluntarily sought a comprehensive assessment at
the University's Counseling andConsultation Services. Relevant
charts were classified into two groups:
· Group 1 (ADHD group) 26 students who received a diagnosis
of ADHD
· Control Group: 28 students who requested a career interest
inventory but did not receive or request any counseling sessions
beyond those needed for the career inventory
Students in both groups completed the Inventory of Common
Problems (ICP). The ICP is an established self-report measure
(inventory) of college student problems that includes 31
questions in seven subset areas. The two subset areas that we
will examine are (1) Academic Problems and (2) Depression. In
each subset area, there were four questions each where a rating
of 1 to 5 was possible. Because of this, within each subset area,
the minimum score was 4 points and the maximum score was 20
points.
a.

What type of observational study did the researchers at the
University of Wisconsin use? Explain.
b.
two dependent (matched pairs)?
c.
Table 1 provides the results for the subset area: Academic
Problems. What conclusion can be made when comparing the
ADHD group to the control group? Why? Can you conclude that
being ADHD causes a student to have a higher score in the
subset area of academic problems? Explain.
Table A1.
Results for Subset Area: Academic Problems (Heiligenstein E.
et al, 1999)
ADHD
Controls
Sample Size (n)
26
28
Mean Score
14.5 points
10.4 points
St Dev (S.D.)
3.7 points
3.9 points
S.E.
.73 points
.74 points
95% C.I. for Population Mean Subset Score
14.5 ± 2(.73) =
14.5 ± 1.5 = approx
(13 to 16 ) points

10.4 ± 2(.74) =
10.4 ± 1.5 = approx
(9 to 12) points
d.
Table 2 provides the results for the subset area: Depression.
What conclusion can be made when comparing the ADHD group
to the control group? Why?
Table A2. Results for Subset Area: Depression (Heiligenstein
E. et al, 1999)
ADHD
Controls
Sample Size (n)
26
28
Mean Score
8.3 points
7.0 points
St Dev (S.D.)
2.5 points
3.2 pointsS.E
.5 points
.6 points
95% C.I. for Population Mean Subset Score
8.3 ± 2(.5) =
8.3 ± 1.0 = approx
(7 to 9) points
7.0 ± 2(.6) =
7.0 ± 1.2 = approx
(6 to 8) points
12.

Are low carbohydrate diets effective? A random sample of six
individuals who wanted to try a low carbohydrate diet was
obtained. Each individual was placed on a low carbohydrate diet
for eight weeks. The weight in pounds was determined for each
individual both before and after the diet, as shown in Table A3.
a.
matched pairs? Explain.
b.
c.
d.
e.
f.
What sample(s) are used to calculate the appropriate confidence
interval?
g.
The following information was obtained from the table found
below.
sample mean difference = 13.2 pounds
S.D. = 13 pounds
standard error (S.E) = 5.2 pounds

sample size (n) = 6 people
Set up the calculation for a 95% confidence interval to estimate
the population mean difference.
h.
Suppose the 95% confidence for the population mean difference
in weight is (2.8 to 23.6) pounds. What conclusion can be made
in this instance about the effectiveness of the diet? Explain in
statistical terms.
i.
What is the advantage of using the differences rather than the
original data in the calculation of the confidence intervals?
Table A3. Weight Before and After Diet
Person
Weight Before Diet
(pounds)
Weight After Diet
(pounds)
Difference in pounds =
(Before-After)
1
125
117
8
2
165
151
14

3
205
169
36
4
115
117
-2
5
138
132
6
6
152
135
17
13.
Two methods of memorizing difficult material are being tested
to determine if one method produces better retention. Nine pairs
of students are included in the study. Each student in the pair
has been matched according to IQ and academic background and
then randomly assigned to use one of the two methods: Method
A or Method B. A memorization test is given to all the students
where the final score can range from 0 to 100 points.
Table A4. Memorization Methods
Sample
95% C.I. for Population Mean Score on Memorization Test
Method A
(50 to 74) points
Method B
(45 to 73) points
Difference = (Method A - Method B)
(1 to 5) points
a.

matched pairs? Explain.
b.
c.
d.
e.
f.
What confidence interval(s) from Table A4 should be used to
compare the memorization score for the two methods? Explain.
g.
Using your answer in the previous part as your basis, state an
appropriate conclusion in terms of the problem.
Please submit this assignment.
6

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