Download Confidence Intervals Mean

Confidence Interval
Estimation for a
Population Mean
Lecture 46
Section 10.3
Wed, Apr 14, 2004
Confidence Intervals


To estimate , we will use confidence
intervals, as we did when estimating
p.
The basic form (as well as the theory)
is the same:
pt. est.  approp. no. of st. devs.
Confidence Intervals


Ifx has a normal distribution, then
the confidence interval is
x  z  (/n)
or
x  z  (s/n).
If (x – u)/(s/n) has a t distribution,
then the confidence interval is
x  t  (s/n).
When to Use Z

If
The population is normal (or nearly
normal) and  is known, or
 The sample size is at least 30,


Then use Z.
When to Use t

If
The population is normal (or nearly
normal), and
  is not known, and
 The sample size is less than 30,


Then use t.
Table IV





Consider again the t table (Table IV).
The degrees of freedom include value
up to 30, then jump to 40, 60, 120.
If the actual degrees of freedom are
between 40 and 60, use 40.
If they are between 60 and 120, use
120.
If they are beyond 120, use z.
Example





See Example 10.5, p. 591 – Cereal
Boxes.
n = 25.
x = 9.82.
Assume that  = 0.29.
Level of confidence = 95%, so z =
1.96.
Example

The confidence interval is
9.82  (1.96)(0.29/25)
= 9.82  0.114
= (9.706, 9.934).
Confidence Intervals on
the TI-83





When the standard normal distribution
applies, do the following.
Press STAT.
Select TESTS.
Select ZInterval.
A window appears requesting
information.
Confidence Intervals on
the TI-83







Select Data or Stats.
Assume we selected Stats.
Enter .
Enterx.
Enter n.
Enter the level of confidence.
Select Calculate and press ENTER.
Confidence Intervals on
the TI-83





A window appears containing
The title “ZInterval”.
The confidence interval in interval
notation.
The sample mean.
The sample size.
Let’s Do It!

Let’s do it! 10.6, p. 593 – How Much
Beverage?
Example


Under the right conditions, we must
use the t distribution.
See Example 10.6, p. 594 – Empty
Seats Imply Dollars Lost.
Confidence Intervals on
the TI-83





When the t distribution applies, do the
following.
Press STAT.
Select TESTS.
Select TInterval.
A window appears requesting
information.
Confidence Intervals on
the TI-83







Select Data or Stats.
Assume we selected Stats.
Enterx.
Enter s.
Enter n.
Enter the level of confidence.
Select Calculate and press ENTER.
Confidence Intervals on
the TI-83






A window appears containing
The title “TInterval”.
The confidence interval in interval
notation.
The sample mean.
The sample standard deviation.
The sample size.
Assignment


Page 598: Exercises 19, 21 – 28.
Page 606: Exercises 43 – 47, 49.