Sample Final Exam MAT 128/SOC 251, Spring 2018
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1 Sample Final Exam MAT 128/SOC 251, Spring 2018 Name: Each question is worth 10 points. You are allowed one 8 1/2 x 11 sheet of paper with hand-written notes on both sides. 1. The CSV file citieshistpop.csv contains the historical population for several north-east American cities. Write a complete Python program that plots the population of New York over time. Assume the CSV file is in the same directory as your.py file. The graph should be a line graph and have a title. citieshistpop.csv: The data in this file comes from::,,, Year,Boston,New York,Philadelphia 1900,560892, , ,670585, , ,748060, , ,781188, , ,770816, , ,801444, , ,697197, , ,641071, , ,562994, , ,574994, , ,590433, , (a) Below are 3 histograms. Each histogram is generated by sampling from the same unknown distribution a different number of times. Draw a sketch of the distribution. (b) Below is a boxplot of some data. Use it to answer the following questions about the data:
2 (i) What is the minimum data value? (ii) What is the maximum data value? (iii) What is the median? (iv) What is the 25th percentile? (v) What is the 75th percentile? 3. Assume the NBA dataset (see last page) has been loaded into the dataframe nba (a) Write a piece of Python code to calculate and print the variance of the number of free throws made by a player during the season. (b) Write a piece of Python code to calculate and print the maximum number of points scored by a starting forward (SF) who is 25 years or older. 4. Assume the NBA dataset (see last page) has been loaded into the dataframe nba (a) Write a piece of Python code that uses the NBA dataset to estimate the probability that a player is a center (position is C) and print this probability. (b) What is the formula for computing the probability that a center player scores more than 800 points in a season? 5. Assume the NBA dataset (see last page) has been loaded into the dataframe nba The following Python code creates a linear model from the data in nba: lm = smf.ols(formula = pts ~ games, data = nba).fit() (a) What is this model predicting? (b) What information is this model using to make the prediction? (c) Running the code print(lm.params) gives the following output: Intercept g dtype: float64 What does the number represent?
3 (d) Write the line of Python code to create and fit a linear model that predicts the number of points scored in a season from the number of games started and the number of free throw points scored in a season. (e) Write a piece of Python code to compute and print out the R-Squared value of your model from part (d). 6. Assume the NBA dataset (see last page) has been loaded into the dataframe nba (a) The correlation matrix for the columns age, games, games started, free throws, and pts in the nba dataframe is shown below. age games games started free throws pts age games games started free throws pts (i) Which two columns are the most correlated? (ii) Which two columns are the least correlated? (b) Write a piece of Python code to compute and print out the mean number of games started in during the season, as well as the 90% confidence interval. 7. (a) Write a complete Python program that computes 500 samples from the normal distribution with a mean of 7 and a standard deviation of 1.5, and plots the samples as a histogram. The histogram should have 15 bins and a title. (b) Suppose the mean length (in inches) of a New York squirrel s tail is 8 with a standard deviation of 0.5. A park ranger randomly catches a sample of 60 squirrels, measures the lengths of their tails, and computes the mean. What distribution does this sample mean come from? Why? 8. This question refers to the NBA dataset on the last page. Our (alternative) hypothesis is that players who start more than 50 games are more likely to score more than 500 points than players who start 50 games or fewer. (a) What is the null hypothesis? (b) To test our hypothesis, we count the number of players in the data meeting a certain criteria and compare it with a histogram. This histogram is made by counting the number of players meeting the same criteria in samples simulated by assuming the null hypothesis is true. (i) When we count the number of players in the data meeting a certain criteria, what was that criteria? (ii) How many players are simulated with one sample?
4 (iii) Assume each simulated player is assigned 1 if they scored more than 500 points and 0 if they scored 500 points or fewer. How do you compute the probability that a player is assigned a 1? (c) The histogram and count from the data (shown as a dashed line on the histogram plot) are below. Would you reject the null hypothesis? Why or why not? 9. The CSV file citieshistpop.csv from Question 1 contains the historical population for several north-east American cities. Write a complete R program that computes and prints out the maximum population of Philadelphia. citieshistpop.csv: The data in this file comes from::,,, Year,Boston,New York,Philadelphia 1900,560892, , ,670585, , ,748060, , ,781188, , ,770816, , ,801444, , ,697197, , ,641071, , ,562994, , ,574994, , ,590433, , Using the ggplot2 library, write a piece of R code to plot the number of games started in a season (x-axis) vs. the number of free throws in a season (y-axis) for all players on the New York Knicks (NYK) and the Brooklyn Nets (BRK). Assume the NBA dataset (see last page) has been loaded into the dataframe nba. The plot should have: the title NYC Team Statistics
5 each data point plotted as a point the points be colored by team NBA Dataset The following dataset is used for questions 3, 4, 5, 6, 8, and 10. It contains statistics on all NBA players for the season. Assume that it has been read in from a csv file and is stored as a Pandas dataframe in the variable nba. player position age team games games started free throws pts Quincy Acy SF 23 TOT Steven Adams C 20 OKC Jeff Adrien PF 27 TOT Arron Affalo SG 28 ORL Alexis Ajinca C 25 NOP Tyler Zeller C 24 CLE The columns are: player = name of NBA player position = position of player (eg. C = center, SF = starting forward) age = age of player team = player s team name, abbreviated games = number of games played by the player in the season games started = number of games started in by the player in the season free throws = number of successful free throws during the season pts = total number of points scored by player during the season
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