MA1530 Project Homework Questions Fall 2017
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School
University Of Arizona *
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Course
1530
Subject
Mathematics
Date
Feb 20, 2024
Type
docx
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3
Uploaded by CaptainCamel2956
Instructions and Questions for MA 1530 Project Homework Fall 2017
Read all of the questions before answering any. This will help you structure your responses. Your responses must be in full, intelligent sentences and paragraphs with proper grammar, syntax, and spelling. This is a formal document. At the same time, this is a math product. I expect to see math in your responses.
Cut and paste each question into your report in order with your response immediately following each question. Please use appropriate spacing to allow an easy identification of question versus answer. You may want to make the questions bold or use a different font. Make sure you KEEP the numbers to the questions. Thanks.
Good luck. You have all of the tools you need to do a great job if you want to. I.
Cover sheet
II.
Each question answered in order
Questions
1.
What is the name of your data set and your sample size for this experiment?
2.
Make a table showing the mean, median, and standard deviation of every variable in your data set. 3.
Make a separate box and whisker charts; one for each variable distance home, distance residence,
and spots. Comment on skewness (or symmetry) of each variable. On your box charts, turn them
horizontal and turn on the mean symbol. 4.
Make side by side (same axes) box and whisker charts of the high school GPA and college GPA. On your box charts, turn them horizontal and turn on the mean symbol. Compare and contrast the statistics
and the box and whisker charts for the high school GPA and college GPA. 5.
Show a histogram of the ages of the subjects in your sample. Comment on the distribution. Unimodal? Bimodal? Multi-modal? Is it representative of the ages of people, in general, who attend a four-year university
? Is this going to be a problem when you try to apply the results of this study to the general population of university students?
6.
Make a Pareto chart showing the proportions of the political ideology of your sample. Find US national proportions from a current reputable source on line. You may not find my exact categories on line, just make intelligent breakouts or consolidations as necessary. Make a table
to compare your data set with national proportions. Is your data set close to national proportions or does it diverge? Why is this a problem (or not)? You need not do any mathematical analysis, just look at the proportions and comment on how adequate your data set replicates (or does not) national proportions.
7.
Comment on how and
why you could
end up with a study sample where the political ideology proportions are strongly divergent away from national averages. 8.
If you were to choose a group of three people (without replacement) at random from your sample, what is the probability that all three liberal (2)? What is the probability that none of them
are of liberal (2)? 9.
What event is the complement to the event “none of them are liberal”? Describe the event in English words. What is the probability of that complementary event? 10.
Using the proportions in your data set, what is the probability that a randomly selected person from your sample is male AND conservative (6) (assuming independence using theoretical probability). 11.
Using the proportions in your data set, what is the probability that a randomly selected person from your sample is either male OR conservative (6) (assuming independence using theoretical probability). 12.
You have selected a person at random. He is male. Given that he is male, what it the probability that he is conservative? For this question, do NOT assume independence; find the actual number of conservative males in your data set (using relative frequency not theoretical probability) and use conditional probability equation accordingly. Show your answer using conditional probability equation as taught in class; do not use any other version thereof. Based on your findings, is P(male) independent of P(conservative). Why? 13.
For the purposes of this study, which variable(s) are explanatory and which variable(s) are response variables? You answer here should, obviously, include every variable in your spreadsheet. Remember that these two categories are mutually exclusive. 14.
Which variables are categorical?
15.
Which variables are quantitative? Which ones are discrete? Which ones are continuous (even if treated
as though they are discrete)?
16.
Construct a correlation table
showing the correlation relationships among all variables. Which three pairs
of variables have the strongest correlations? Also, identify the variable with which “newspapers” is most strongly correlated.
17.
Construct a scatter plot of the
pair of variables that is most highly correlated. Comment.
18.
Conduct linear regression. First do it using “college GPA” as the response variable and using age, gender, high school GPA, distance home, distance residence, TV, sports, and newspapers as explanatory variables. What is the formula you have obtained? Comment about your r
2
value.
19.
Find the subject person #21 in your data set. Describe subject #11. Using your regression formulae from above, predict his/her college GPA. 20.
Compare this prediction to the actual observed value for subject #21. Calculate the residual value for this person. Based on this residual, was the formulae very good at predicting the output for this person?
21.
In any normal distribution, how much of the probability is contained within µ+/- 1σ?...within µ+/- 2σ?...within µ+/- 3σ? What is the mean of the standard normal distribution? What is the standard
deviation of the standard normal distribution? 22.
Assume, for a moment, that the hours spent watching TV (“TV”) are normally distributed. Using the statistics from your sample as the population parameters, find the number of hour such that 25% of the population watches more than that number. Find the number of hours such that 45% watch less. 23.
If you were to see the real
distribution of how much Americans watch TV, it would not be normal. Describe what you think it would look like and why.
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