Making Decisions about a Population Mean with Confidence

1
Chapter 10

• Making Decisions about a Population Mean with
  Confidence

2
z-test vs. t-test

• The z-test is what we have grown to know and
  love. The problem is that you need to know the
  standard deviation. Thats what makes the .
• t-test so fantastic. You dont need to know
  standard deviation, just sample size. Now we
  have a new distribution, the t-distribution.

3
The t-distribution

• The t distribution has a symmetric bell-shaped
  density function centered at 0, but has standard
  deviation gt 1.
• The t distribution approaches the N(0,1)
  distribution as n (the sample size) increases.
  For n greater than 30 there is only a small
  difference between them.

4
Student t Distributions for n 3 and n 12
t
0
Page 575
5
Standard Error

• When we use data to estimate the standard
  deviation of a statistic, the result is called
  the standard error of the statistic.

6
Lets Do It

• LDI 10.1, p. 568
• Ex. 10.2, Waste Data, p.575

7
Student t Distribution

• If the distribution of a population is
  essentially normal, then the distribution of

8
t -Test

• Use page 579 as an outline.
• Keep in mind that t is the test statistic and
  that large values of t will cause us to reject
  the null and accept the alternate.

9
Lets Do It

• Page 580 Example 10.3
• Page 582 LDI 10.3
• Page 583 LDI 10.4

10
Homework 19

• LDI 10.1, 10.3, 10.4, Ex 10.2, 10.3
• Exercises 10.1, 10.3, 10.7, 10.13, 10.16a

11
CI for the Mean (page 591)

• Confidence interval for the mean is given by
• The margin of error is given by

12

• The amount reported lost for a random sample of n
  20 pickpocket offenses occurring in Rome are
  given here
• Does the data meet the assumptions of doing a 95
  CI for the mean? If so, construct and interpret
  it. (10.21)

13
Lets Do It

• Ex. 10.6 p. 594
• Page 596 LDI 10.7
• Page 603 LDI 10.10

14
Homework 20

• LDI 10.7, 10.8, Ex.10.6
• Exercises 10.14, 10.20, 10.22, 10.27, 10.31