Solution
STAT 500 Homework 1 Solution (Penn State University) Latest Verified
Review 2023 Practice Questions and Answers for Exam Preparation, 100%
Correct with Explanations, Highly Recommended, Download to Score A+
Homework 1 (Eleven problems) [Lessons 1,2]
SOLUTIONS
Problem 1 (5 points):
Study 1: A British study compared 966 patients with brain cancer to 1716 patients without brain cancer.
The patients’ cell phone use was measured using a questionnaire. Cell phone use for the two groups
was similar.
Study 2: A study published in The Journal of the American Medical Association (Volkow et. Al., 2011),
indicates that cell phone use speeds up activity in the brain. As part of a randomized crossover study, 47
participants were fitted with a cell phone device on each ear and then underwent two positron emission
topography, or PET, scans to measure a specific type of brain activity. During on scan, the cell phones
were both turned off. During the other scan, an automated 50-minute muted call was made to the
phone on the right ear. The order of when the call was received (for the first or second scan) was
randomized. Comparison of the PET scans showed a significant increase in activity in the part of the
brain closest to the antenna during the transmission of the automated call.
A) What type of studies, observational or experimental, are the two studies listed above?
Study 1: Observational – no random assignment of treatment
Study 2: Experiment – there was random assignment of a treatment
B) For each study identify the response variable and explanatory variable.
Study 1: Response was whether or not the subject developed brain cancer and Explanatory was cell
phone usage
Study 2: Response was specific type of brain activity while the call is being received and Explanatory
was whether or not the automated call was placed to the phone on the right ear
Problem 2 (5 points):
A March 2011 Gallup poll reported that 60% of Americans favored offshore drilling as a means of
reducing U.S. dependence on foreign oil. The poll was based on the responses of n = 1021 individuals
and resulted in a margin of error of approximately 3%. Find the approximated margin of error had the
poll been based on a sample of size:
1
, Solution
a) 1/sqrt(100) = 0.10 or 10%
b) 1/sqrt(400) = 0.05 or 5%
c) 1/sqrt(1600) = 0.025 or 2.5%
d) The sample sizes increased by a factor of four with effect of cutting the margin of error in half.
e) As the sample size increases the margin of error decreases
Problem 3 (5 points):
A researcher wants to compare student loan debt for students who attend four-year public universities
with those who attend four –year private universities. She plans to take a random sample of 100 recent
graduates of public universities and 100 recent graduates of private universities. Which type of random
sampling is utilized in her study design? Used stratified sample
Problem 4 (5 points):
If you want to conduct a study with humans to see if cell phone use makes brain cancer more likely,
explain why an observational study is more realistic than an experiment.
An experiment would not be practical for ethical reasons.
Problem 5 (5 points):
Without using technical language, explain the difference between observational and experimental
studies to someone who has not studied statistics. Include in your explanation a primary advantage of
using an experimental study to an observational study.
In and OS, we observe subjects in the groups they are already in; for experiment we randomly assign
subjects to treatment groups (or randomly assign the treatments to subjects).
Problem 6 (5 points):
Identify each of the following as either categorical or quantitative. If categorical is it binary, nominal, or
ordinal? If quantitative is it continuous or discrete? Finally, provide one graph choice that would be
best choice to display the data.
A) Number of pets in family: quantitative, discrete – histogram, stemplot, boxplot
B) County of residence for in-state (PA) students categorical, nominal – pie or bar graph
C) Distance in miles PSU employees travel for work quantitative, continuous – histogram, stemplot,
boxplot
D) Time spent last month attending a place of religious worship quantitative, continuous - histogram,
stemplot, boxplot
2
STAT 500 Homework 1 Solution (Penn State University) Latest Verified
Review 2023 Practice Questions and Answers for Exam Preparation, 100%
Correct with Explanations, Highly Recommended, Download to Score A+
Homework 1 (Eleven problems) [Lessons 1,2]
SOLUTIONS
Problem 1 (5 points):
Study 1: A British study compared 966 patients with brain cancer to 1716 patients without brain cancer.
The patients’ cell phone use was measured using a questionnaire. Cell phone use for the two groups
was similar.
Study 2: A study published in The Journal of the American Medical Association (Volkow et. Al., 2011),
indicates that cell phone use speeds up activity in the brain. As part of a randomized crossover study, 47
participants were fitted with a cell phone device on each ear and then underwent two positron emission
topography, or PET, scans to measure a specific type of brain activity. During on scan, the cell phones
were both turned off. During the other scan, an automated 50-minute muted call was made to the
phone on the right ear. The order of when the call was received (for the first or second scan) was
randomized. Comparison of the PET scans showed a significant increase in activity in the part of the
brain closest to the antenna during the transmission of the automated call.
A) What type of studies, observational or experimental, are the two studies listed above?
Study 1: Observational – no random assignment of treatment
Study 2: Experiment – there was random assignment of a treatment
B) For each study identify the response variable and explanatory variable.
Study 1: Response was whether or not the subject developed brain cancer and Explanatory was cell
phone usage
Study 2: Response was specific type of brain activity while the call is being received and Explanatory
was whether or not the automated call was placed to the phone on the right ear
Problem 2 (5 points):
A March 2011 Gallup poll reported that 60% of Americans favored offshore drilling as a means of
reducing U.S. dependence on foreign oil. The poll was based on the responses of n = 1021 individuals
and resulted in a margin of error of approximately 3%. Find the approximated margin of error had the
poll been based on a sample of size:
1
, Solution
a) 1/sqrt(100) = 0.10 or 10%
b) 1/sqrt(400) = 0.05 or 5%
c) 1/sqrt(1600) = 0.025 or 2.5%
d) The sample sizes increased by a factor of four with effect of cutting the margin of error in half.
e) As the sample size increases the margin of error decreases
Problem 3 (5 points):
A researcher wants to compare student loan debt for students who attend four-year public universities
with those who attend four –year private universities. She plans to take a random sample of 100 recent
graduates of public universities and 100 recent graduates of private universities. Which type of random
sampling is utilized in her study design? Used stratified sample
Problem 4 (5 points):
If you want to conduct a study with humans to see if cell phone use makes brain cancer more likely,
explain why an observational study is more realistic than an experiment.
An experiment would not be practical for ethical reasons.
Problem 5 (5 points):
Without using technical language, explain the difference between observational and experimental
studies to someone who has not studied statistics. Include in your explanation a primary advantage of
using an experimental study to an observational study.
In and OS, we observe subjects in the groups they are already in; for experiment we randomly assign
subjects to treatment groups (or randomly assign the treatments to subjects).
Problem 6 (5 points):
Identify each of the following as either categorical or quantitative. If categorical is it binary, nominal, or
ordinal? If quantitative is it continuous or discrete? Finally, provide one graph choice that would be
best choice to display the data.
A) Number of pets in family: quantitative, discrete – histogram, stemplot, boxplot
B) County of residence for in-state (PA) students categorical, nominal – pie or bar graph
C) Distance in miles PSU employees travel for work quantitative, continuous – histogram, stemplot,
boxplot
D) Time spent last month attending a place of religious worship quantitative, continuous - histogram,
stemplot, boxplot
2
