Statistics Projected (To be done on R Studio)

STAT 381 Fall 2020

Final Project Version 5 Project Description

DUE DATE: WEDNESDAY, DECEMBER 9, 2020 by 11:00 AM on Gradescope

Project Goal:

Practice working with real data. Calculating a confidence interval / bound. Performing a hypothesis test.

Dataset Descriptions:

• Dataset SAT Reading.csv: The dataset contains the average SAT Reading scores for randomly selected colleges and universities in Delaware, the District of Columbia, Maryland, Pennsylvania, Virginia, and West Virginia in 2011.

• Dataset SAT Math.csv: The dataset contains the average SAT Math scores for randomly selected colleges and universities in Delaware, the District of Columbia, Maryland, Pennsylvania, Virginia, and West Virginia in 2011.

Data Source: StatCrunch, by Pearson, www.statcrunch.com

Dataset File:

The dataset may be found as a .csv file. They are named Dataset SAT Reading.csv and Dataset SAT Reading.csv. There is a header in the datasets.

Assignment Details:

• Work on this project INDIVIDUALLY. You may receive assistance (but not solutions) from Te- aching Assistants and the Instructor. You are allowed to reference Blackboard, MyOpenMath, Gradescope, your notes, the course textbook, R documentation, and previous projects / home- work for assistance.

• You cannot work in teams. You cannot work side-by-side, you cannot submit someone else’s work (partial or complete) as your own. The University’s policy is available here: https://dos.uic. edu/conductforstudents.shtml

• In particular, note that you are guilty of academic dishonesty if you extend or receive any kind of unauthorized assistance.

• Absolutely no transfer of program code or files between students is permitted (paper or electronic), and you may not solicit advice or solutions from family, friends, online forums, or websites including, but not limited to Chegg.

• Other examples of academic dishonesty include emailing your program or files to another student, copying-pasting code from the internet, working in a group, and allowing a tutor, TA, or another individual to write an answer for you.

• Academic dishonesty is unacceptable, and penalties range from a letter grade drop to expulsion from the university. Cases are handled via the official student conduct process described at https://dos.uic.edu/conductforstudents.shtml.

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Directions:

• Submit your project on Gradescope under “Final Project” under the correct version number.

• Project must be typed for full credit. Submit your project as a PDF file.

• Answers without code will not receive full credit. Code without answers will not receive full credit.

• For the hypothesis test / confidence interval (or bound), in addition to supplying code, provide the formulas R used to calculate

– the test statistic;

– the degrees of freedom;

– the p-value;

– the confidence interval (or bound).

You do not need to plug-in values. Just report the formula.

• Provide appropriate commentary where needed.

• Length expected to be between 2 and 4 pages, but no penalty will be imposed if you are outside these guidelines.

Notes:

• No late projects will be accepted unless you provide (acceptable) documentation as to why the assignment is late.

• Internet outages must have documentation in order for the project to be accepted.

• Projects will not be accepted via email.

• Points will be deducted if project not submitted to the correct version.

Project Grading (63 points):

Part 1: 3 points Part 2: Histograms

• a) 7 pts code + 1 pt graph

• b) 2 pts

• c) 2 pts code + 1 pt results

• d) 4 pts code + 3 pts re- sults

• e) 1 pt

Part 3: Hypothesis Test

• a) 7 pts

• b) 7 pts code

• c) 1 pt

• d) 3 pts

• e) 4 pts code + 1 pt results

• f) 4 pts

• g) 1 pt

• h) 2 pts

• i) 1 pt

• j) 1 pt

Part 3: Confidence Interval / Bound: 7 pts

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Tasks:

1. Part 1: Import your datasets into R and save them. There is a header in each of the datasets. Provide your code.

2. Part 2: Use the Dataset for the Reading SAT. Provide your code for parts a, c, d. Provide your histogram for part a. Provide your answers to parts b, c, d, e.

(a) Make a histogram of your data with frequency on the y-axis. Break up the bins into the intervals [450, 500), [500, 550), [550, 600), . . . , [750, 800). The y-axis should go from 0 to 60.

(b) Describe how your histogram looks by:

• Stating whether it is relatively symmetric or not. • Stating whether it is unimodal, bimodal, multimodal, etc.

(c) Report the five number summary of your data.

(d) Report the sample mean, the sample standard deviation, and the sample size. If you decide to round, round to 3 decimals.

(e) Is the sample size large enough so that we will not have any issues with the Central Limit Theorem?

3. Part 3: Perform a hypothesis test to answer the following question.

We want to compare the average Reading SAT Score to the average Math SAT Score. University Administrators want to know if the average SAT Math Score is higher than the average Reading SAT Score by more than 2.25 points.

Use α = 0.076 to make your decision. Describe how you would make your decision using both p-values and critical regions. Be sure to state / provide

(a) the hypotheses;

(b) the R Code;

(c) the R Code Results;

(d) the test statistic value;

(e) the critical value (calculated using R);

(f) the critical region;

(g) your decision using critical regions;

(h) the p-value;

(i) your decision using p-value’s;

(j) your conclusion.

In addition to performing the hypothesis test, obtain the confidence interval / bound associated with the given level of significance. State the parameter the confidence interval is for. Write an interpretation of your confidence interval / bound.

For the hypothesis test / confidence interval (or bound), in addition to supplying code, provide the formulas R used to calculate

• the test statistic; • the degrees of freedom;

• the p-value; • the confidence interval (or bound).

You do not need to plug-in values. Just report the formula.

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