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Name: Student #: Due: April 4 @ 10:05 AM – Submit through Crowdmark on Blackboard
Remember to show all your work in the assignment. Solutions without justifications
will not earn any marks. Your assignment should consist of a document or image of your
answers/analysis/explanations, followed separately by a PDF file of your R code with appropriate comments for your work as an appendix item in each question that used R.
Do not submit just the R code with embedded outputs. All the R code needed has been
provided for you either in the assignment or under ‘Course Materials’ on Blackboard.
Note that contextual problems should include some form of conclusion or interpretation, not
just a numerical answer!
The goal of the assignments is to assess whether you can apply the concepts discussed
in lecture. While there may be different paths to the solution, it is your responsibility
to demonstrate in your solutions that you have learned and can apply the course material
appropriately. This includes verifying any assumptions as necessary.
Problem 1 [20 marks]. A local product manager is under the impression that the three
local factories have the same production efficiency and hourly outputs. The regional product
manager believes otherwise and decided to study the hourly outputs between factories A, B,
and C over eight days. The data is recorded below:
Factory
A B C
24 37 36
31 34 33
35 35 33
18 39 37
32 44 32
33 38 28
27 36 38
27 34 30
27 35 35
26 51 30
a) (6 points) State the appropriate null and alternative hypotheses. Use side-by-side
boxplots to verify the assumptions before proceeding. Comment on what the boxplots
1 tell you about the assumptions. You may use R to construct your boxplots, be sure to
label appropriately. A plot should convey all necessary information without words!.
b) (14 points) Does the collected data support the claim that all three factories have the
same hourly outputs? Show all your work, state and interpret your p-value. Describe
one extraneous variable in this study. This problem should be done by hand.
Problem 2 [20 marks]. Use R to answer this problem. Download the Olympics.csv
data set on Blackboard Dataset obtained from the Journal of Statistics Education
(http://ww2.amstat.org/publications/jse). Used by permission of author.
You can read the data set into R by selecting the file from your downloads:
c d t<?r e a d . c s v ( f i l e . c h o o s e ( ) , h e a d e r=T) You can read more about the format of the data and variable descriptions here, scrolling
down to London 2012 Olympics Data. We will be using this data to examine the possible
relationship between a country’s GDP and the total number of medals won during the London
2012 Olympics.
a) (3 points) In your own words, describe (or hypothesize) what association, if any, there
might exist between a country’s wealth and their performance in the olympics. What
would be a purpose to modeling this possible association?
b) (4 points) Fit a simple linear regression in R to model the response Total Medals
against the predictor GDP (measured in $10 trillion). What is the regression line?
Interpret the estimates b0 and b1 in this context – what do they measure?
c) (8 points) Produce the 4 diagnostic plots that we discussed in class and use them to
comment on the assumptions and appropriateness of the model for this data.
d) (5 points) Assuming the model is appropriate, predict the number of medals a fictional
country would earn, if their GDP is $9 billion for the year of 2012. Produce an
appropriate interval for your estimate, and interpret. Marijuana Use Problem 3 [12 marks]. In this problem, you will be examining data to determine if an
association exists between marijuana use and dance or party participation. Dataset obtained
from (http://www.stat.ufl.edu/ winner/datasets.html). You can read more about the format of the data and variable descriptions here. The study was conducted to determine if
behaviour correlates with marijuana use among middle class youths and was published in
1976 (a bit outdated but interesting nonetheless!). The data is summarized below: Never
<1/month
>1/month
>1/day
Col. Totals Party/Dance Participation
Not At All Somewhat A Great Deal
40
213
118
3
55
40
1
44
54
0
17
32 2 Row Totals a) (8 points) State the null and alternative hypotheses and perform an appropriate test
for association. State and interpret your p-value and conclusions.
b) (4 points) Do you think this was an experimental study or an observational study,
why or why not? Can the results of this study be generalized to the population? Can
we conclude any causal relationships? 3
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The post submit just the R code with embedded outputs. All the R code needed has been provided for you either in the assignment or under ‘Course Materials’ on Blackboard. appeared first on Wise Papers.
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