Download whenever you are asked to perform inference, it is implied that you

Guiding Questions Section 8.3
Assignment: 55,57,59,63,65,67,71,73,75-78
Name: _____________
What are the objectives for this lesson?
One-sample z interval for a population meant distributiondegrees of freedom (df)standard error of the sample mean –
one-sample t interval for a population mean –
robust To calculate a 95% confidence interval for µ, use the formula: _______________________________
Reminder to check the conditions for inference ( __________,___________,__________) are satisfied and the standard
deviation σ is known, we can use this method to construct a confidence interval for µ.
One-Sample z Interval for a Population Mean
The critical
value, z* = 1.96
is used for 95%
confidence.
The critical value z* is found from the standard Normal distribution.
In many practical settings, if we do not know µ, we would not know σ either. We can, however, use a _______
_________ for the population standard deviation σ from a similar study that was done in the past or from a small-scale
Reminder to
pilot study. Then follow these steps:
always round
up when
finding n.
*
*
*
We are learning the materials in this chapter to help with planning for a study. You may find the results for the sample
size to be unrealistic to get the margin of error desired and need to re-examine. Re-read the problem How Many
Monkeys? to see the connection.
Check Your Understanding pg 501
When we standardize, we subtract the mean and divide by the standard deviation.
For a sampling distribution that is close to Normal, the formula would be:
If we do not know the standard deviation σ, we can estimate by using the sample standard deviation sx.
When we standardize using sx , the formula would be:
Calculator Bingo Activity will be done in class. The colon in the formula tells calculator to execute each command in
order with the push of a single button!
The t Distributions; Degrees of Freedom
Carefully highlight each of the graphs on the left. Then describe the
similarities between t distributions and the Normal curve below.
Check Your Understanding pg 507 lets you practice finding critical values t* in the table in the back of your text.
Practice checking with calculator function.
a)
b)
c)
Standard error of the sample mean
One-Sample t Interval for a Population Mean
What conditions need to be met for inference about a population mean?
_________________
________________
___________________
WHENEVER YOU ARE ASKED TO PERFORM INFERENCE, IT IS IMPLIED THAT YOU USE THE
FOUR-STEP PROCESS. PUT A STAR BY YOUR NAME ON THE TOP OF YOUR PAPER IF YOU
READ THESE SENTENCES.
Checking Normal see top of page 509---these should ring a bell‼
Inference for __________ uses z; inference for _________ uses t.
If the sample size is off the chart for Table B, use the highest df available that is less than your desired df. Better yet, use
a calculator to get the accurate value of t* for any df.
Check Your Understanding pg 511
1.
2.
3.
4.
Note about robust. The t procedures are not robust against outliers. Why? _____________________________________
Using One-Sample t Procedures: The Normal Condition
*
*
*
AP Exam Common Error- Many students incorrectly state the Normal condition by saying that the sample must have a
Normal distribution. This isn’t true (or even possible!). Instead, we use the sample data to make an inference about the
shape of the population from which the sample came.
AP Exam Common Error—Simply saying that we “assume Normality” will not earn full credit when the data are
provided. Students must show a graph and give an appropriate comment that addresses the Normality of the
population.
AP Exam Common Error- If you compute a confidence interval and also find one on the calculator and list both, these
are considered parallel solutions. If the answers are not the same, you will get the lower score of the two.