

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. Timetable: (LEC1) Tues 10:0011:30 MRT 251 (LEC2) Thurs 8:3010:00 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. 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 This test will be an open book multiple choice test. Homework:
Submit homework on Fridays. Late assignments will not be graded 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:
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 6.17 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 R_{1} is drawn from a production lot
with a normal distribution having mean 100 ohms and 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 6.22, 6.26, 6.218 Exercise 2: Generate c1c5 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 (Xbarmu)/(s_{X}/sqrt{n}) is exactly the same as Zbar/(s_{Z}/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 ttables (pick the 90th and 95th percentiles for the comparison). Use the calculator to calculate the pivot whose distribution is a X2 statistic; i.e (n1)s^{2}_{Z}. Make a histogram of the result and compare this with the X2tables (pick the 90th and 95th percentiles for the comparison). Exercise 3: From the text do 6.48 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: 6.412, 6.52, 6.62, 6.6126.76, 6.712 Exercise 2: Use the boostrap confidence macro above to redo problem 6.48. 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 tbootstrap 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: 6.86, 6.816, 6.1112 (do the confidence interval for beta by hand but check with minitab) Homework #5 is due March 13 From the text do: 6.114,6.118, 6.1114, 6.1210, 6.104, 6.1014 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: 8.18, 8.118, 8.28, 8.212, 8.218, 8.38, 8.318 Also do 8.54, 8.510, 8.514, 8.610 Solution HW6 We finished off with power and the NeymanPearson lemma. Next Tuesday's class is moved until shortly before the final. The final class is next Friday.
