Assignment for Monday, March 6, 2006 (M 358K, Smith)
Students whose last names begin with M - Z will be called on today.
I. Read Section pp. 380 - 396.
- Be sure to read carefully, since the concepts in Chapter 6 are central ideas in most of the rest of the course.
- Read carefully and remember the "caution" on p. 383.
- Note the last paragraph before Section 6.1 on p. 383: This
chapter is intended to give you an idea of the basic statistical
interence concepts, without dealing with the additional complication
involved in the fact that we cannot expect to know sigma in practice.
That additional complication will be addressed in the next chapter,
after you have had a chance to chew on what is in Chapter 6.
- Try the confidence interval applet (p. 386)
- Be especially careful in reading and understanding the
definition of Confidence Interval on p. 387. A lot of people have a
tendency to try make the concept simpler than it is. Don't fall into
this trap.
- When you read the box on p. 388, go back and read the box on p. 387. Try to put the two together.
- Be sure to read carefully and heed the cautions on pp. 393 - 394.
- The last paragraph before "Beyond the Basics" on p. 394 is
especially important for understanding (and avoiding misunderstanding.)
Be sure to read it carefully, slowly, more than once, and impress it
upon your memory.
II. Do the follow exercises to reinforce reading and for possible class discussion.
p. 396 #6.1 - 6.3, 6.5, 6.9, 6.13, 6.20, 6.21, 6.25, 6.26, 6.29 (Note:
Some of you may need to use the ideas in Exercises 6.26 and 6.29
in your class projects.)
III. Also do the following exercise to reinforce reading and to discuss
in class: Which of the following accurately describe what "(1.5, 2.3)
is a 90% confidence interval for the mean µ" means? Explain what
is wrong with those that are not accurate.
a. The probability that 1.5 < µ < 2.3 is .90.
b. 90% of the time, µ will be between 1.5 and 2.3.
c. In calculating the confidence interval, we used a method that, in
repeated sampling with simple random samples of the same size, will
give an interval containing µ about 90% of the time.
d. In calculating the confidence interval, we used a method which for
about 90% of all possible simple random samples of the same size will
give an interval containing µ
e. In repeated sampling, the sample mean will lie in the interval (1.5, 2.3) for about 90% of all samples.