MAT 2375 

Introduction to Statistics

Theory of statistical inference; point and interval estimation, tests of hypotheses. Inferences about normal models. Introduction to nonparametric methods.

Prerequisite: MAT2371.

Professor :  D. McDonald
209-585 King Edward
Telephone: 562-5800 x 3505
Email: dmdsg@uottawa.ca

Timetable:

(LEC1)     Tues 10:00-11:30         MRT 251

(LEC2)     Thurs  8:30-10:00       MRT 251

 Help Session before the final:  Friday April 18th at 14:00 MRT 256 - please note the room change!

Text : Probability and Statistical Inference 7th Ed.
Hoag and Tanis edited by Prentice Hall

Exam topics:

6.1, 6.2, 6.4,  6.5, 6.6, 6.7, 6.8, 6.9, 6.10, 6.11, 6.12 (just prediction intervals)

8.1,  8.2, 8.3,  8.5,  8.6, 9.1

You can expect a number of plug in type problems: write down the general formula and give numerical values for the factors in the formula.

There are two development questions with multiple parts.

The final is open book - notes text and whatever you want to bring. Bring a simple calculator.

Departmental Help 

Office Hours: Wednesday, 10:00 - 11:30, or by appointment.

Midterm:  Scheduled February 26

This test will be an open book multiple choice test.

Homework: Submit homework on Fridays.  Late assignments will not be graded

Final Examination : Three hours, open book

Final Grade : If the grade on the final examination is less than 40% then that is the final grade. If the grade on the final is  40% or more then the final grade is calculated as:
Homework: 25% 
Midterm Test:  25%
Final Examination:  50%
Total : 100%

NOTE: The midterm grade will be replaced by the grade on the final if the later is higher. However, if you miss the midterm without a medical certificate or an equivalent written justification then the midterm grade will be zero and it won't be replaced.


Homework : A numerical answer without an explanation is not a complete solution to a problem.
Solutions will be available on this web page.

Syllabus :

Week One #1: We discuss the course outline and start by discussing the purpose of this course.  This gives us a chance to review discrete and continuous distributions, the normal histogram and the central limit theorem. 

Week One #2: We will discuss summary statistics and the use of Minitab.

Homework #1

Exercise 1: Do 6.1-7 and make a histogram by hand of the same data.

Exercise 2: Go to the NOAA web site: http://seaboard.ndbc.noaa.gov/historical_data.shtml

 a)  Download 2006's weather data and notice that these are readings taken from a floating weather buoy many times a day.  Pick out the readings of air temperature ATMP in the afternoon of the month of June and make a histogram  and give the summary statistics. Do the same for January. Specify which weather station you selected and which year you picked.

b) Do the same thing for 1990.  

c) Do you detect some global warming?

Exercise 3: The resistor R1 is drawn from a production lot with a normal distribution having mean 100 ohms and
standard deviation equal to 10 while resistor R2 is drawn from a production lot with a exponential distribution having mean 200 ohms. Recall that the effective resistance of two resistances R1 and R2 wired in parallel is 1/R=1/R1+1/R2.
Use Minitab to simulate 1000 devices containing pairs of resistors R1 and R2 which are wired in parallel giving effective resistance R.
From this simulated sample, estimate the proportion of devices that we will produce in future with:
1- R>75.
2- 60<R<65.

Homework #1 is due January 17th  Solution HW#1

Week Two  #1: We introduce a statistical model and introduce estimation theory. 

Week Two #2: The MLE.

Homework #2 is due Jan 31 Solution HW#2

Exercise 1: From the text do 6.2-2, 6.2-6, 6.2-18

Exercise 2: Generate c1-c5 with 5000 rows of normals with mean 10 and standard deviation 2. Equivalently forget the 10 and 2 and generate standard normals.  We showed the pivot (Xbar-mu)/(sX/sqrt{n}) is exactly the same as Zbar/(sZ/sqrt{n}) anyway. Use Minitab to calculate the average of the 5 values and the standard deviation.  Then use the calculator to calculate the pivot whose distribution is a t statistic. Make a histogram of the result and compare this with the t-tables (pick the 90th and 95th percentiles for the comparison). Use the calculator to calculate the pivot whose distribution is a X2 statistic; i.e (n-1)s2Z. Make a histogram of the result and compare this with the X2-tables (pick the 90th and 95th percentiles for the comparison).

Exercise 3: From the text do 6.4-8

Week Three:  Confidence intervals for means, proportions 

Week Four: Bootstrap confidence intervals Confidence intervals for differences of means and variances.

Homework #3 is due February 7th  Solution

Exercise 1: From the text do: 6.4-12, 6.5-2, 6.6-2, 6.6-126.7-6, 6.7-12

Exercise 2: Use the boostrap confidence macro above to redo problem 6.4-8.  You will have to copy the macro to a file using notepad and save it in C:/temp as  firstboot.mac for example.  Note that on the web I gave the file an extension txt because the mac extension has been reserved for multimedia extensions using quicktime.Enter the data into C1. Call the macro by % C:/temp/firstboot C1 C2.  This will output 2000 values of the t-bootstrap into C2. Print a histogram. Find the 5th and 95th percentiles of this bootstrap distribution. Use these percentiles instead of those of a t(4) to make a 90% confidence interval..

I hope this works.  It works in my office and it works in class. 

Week Five: Design of experiments - confidence intervals when observations are paired. Regression

Homework #4 is due February 14th Solution HW4

From the text do: 6.8-6, 6.8-16, 6.11-12 (do the confidence interval for beta by hand but check with minitab)

Solution to the Midterm

Homework #5 is due March 13 

From the text do: 6.11-4,6.11-8, 6.11-14, 6.12-10, 6.10-4, 6.10-14 Solution HW5

The following Macros allow one to carry out a Fisher exact test: Macro, Submacro

Homework #6 is due April 3 

From the text do: 8.1-8, 8.1-18, 8.2-8, 8.2-12, 8.2-18, 8.3-8, 8.3-18

Also do 8.5-4, 8.5-10, 8.5-14, 8.6-10 Solution HW6

We finished off with power and the Neyman-Pearson lemma. Next Tuesday's class is moved until shortly before the final.  The final class is next Friday.