# Are you ready for Stat 541?

## Statistics Course prerequisites

As the name implies, STAT 541 is a second course in statistics and thus assumes as prerequisite a basic knowledge of statistics such as would be gained in an introductory undergraduate statistics course. At SDSU, this course would be STAT 281 Introduction to Statistics.

If you enroll in STAT 541 without this knowledge, you should expect the course to be challenging and time consuming, with the possibility of a poor grade being real.

## Computer prerequisites

According to the “customer‐oriented” design of the class, STAT541 will extensively rely on the use of computers and computer generated results. Students are expected to know how to perform basic operations involving their computers, such as:

• Open, edit, save a MS Word document (or a document in the text editor of their choice);
• Open, edit, save an MS Excel document (or a document in the table editor of their choice);
• Copy/paste text and images between software packages

### R software package

STAT 541 will extensively rely on the R software package to present and perform statistical analyses in class. Students are not required to use R; they may use the statistical software of their choice. However, R has advantages such as being free, opensource and the software of choice in many scientific disciplines, thus will be used by the instructors in this class in order to provide a common software platform for discussion.

A brief introduction to R will be given to the students. However, some basic knowledge of R and R studio is strongly encouraged. Such foundational knowledge can be obtained by taking the one credit online STAT 414 R Programming class.

## Statistical Knowledge Prerequisites

Essential concepts: Understanding of the statistical concepts listed below is assumed in STAT 541.

Coverage of all of these concepts is contained in the opening chapters of the STAT 541 text, Freund R.J.,et al, Statistical Methods (3rd Ed.), Elsevier, 2010. These chapters are not covered in STAT 541. The essential concepts are:

1. Variable types and random variables (Chapter 1 of STAT 541 textbook).
2. Discrete, Binomial, Poisson and Normal distributions (Chapter 2 of STAT 541 textbook)
3.  t, F, χ2 and mean sampling distributions (Chapter 2 of STAT 541 textbook)
4. Hypothesis testing (in particular: type I and II errors, p‐value and significance levels) (Chapter 3 of STAT 541 text)
5. Inference for Two Populations (in particular Inference on the difference between means (Section 5.2 of text)

### Self Test of Prerequisite Statistical Knowledge

If you cannot answer all of the questions correctly, you do not have the pre‐requisite knowledge needed to take the class and should take action to correct deficiencies before beginning STAT 541. If you have previously taken a course equivalent to SDSU’s STAT 281, you should either review the material by self‐study or take STAT 281. If you have never previously taken such a course, you must take STAT 281 or equivalent. STAT 281 is available online and in the classroom every fall, spring and summer semester.

When taking this test, you may use:

1. non‐programmable personal calculator (no smartphone);
2. textbook

Time: 30 minutes

Instructions:

• Read the questions in their entirety and pay attention to the wording!
• Clearly define what information is provided, and what is demanded.
• Write down (clearly) all the steps that you use to reach the solution

Q1: The grades of 10 students are listed below. Test the hypothesis that the average of the class is significantly different than 70 (at 0.05 confidence level). Provide the following data:

1. The sample average and variance;
2. Hypotheses that you are testing
3. Equation and value for the test statistic that you are using
4. The value for the rejection region at 0.05 confidence level
5. An approximation of the p‐value for the test statistic
6. Interpretation of the result of the test (which hypothesis do you support?)
Student number12345678910

Q2: The grades of 10 students at the beginning and the end of the semester are listed below. Assume that the sample variances for the grades at the beginning and end of the semester are equal. Test the hypothesis that the average improvement for the class is significantly larger than 10 (at 0.05 confidence level). Provide the following data:

1. The relevant average and relevant sample standard deviation;
2. Hypotheses that you are testing
3. Equation and value for the test statistic that you are using
4. The value for the rejection region at 0.05 confidence level
5. An approximation of the p‐value for the test statistic
6. Interpretation of the result of the test (which hypothesis do you support?)
Student Number12345678910
Beginning71707473736978697668
End87879086858581808485

Q3: Find the value for the following probability, where Z follows a standard normal distribution:

Pr( -1.96 < z < 1.96) =