1. Ch. 8 Estimating with Confidence
Ch. 8-1 Confidence Intervals: The Basics

2. confidence intervals
significance tests
confidence intervals
significance tests
Introducing confidence intervals visually. I need a volunteer.

3. current AP Stats students𝜇
4 students 𝑥
Let’s take a sample of 4 and find 𝑥
Based on our sample, we estimate the mean exam score is ___

4. point estimator
statistic
parameter
point estimate
What does this remind you of?
Ch. 7 sampling distribution
Sampling Distribution of 𝑥
normal because pop. dist. is normal
N(𝜇, 𝜎 𝑥 )
𝜇 (unknown mean)
= =5
𝜎 𝑥 = 𝜎 𝑛 𝜇
10% condition
2 5 =10
𝑛≤ 1 10 𝑁 4≤ 10

5. ______ 10 Write this every time!! ____ ±10= , REMEMBER THE WORDING!!
____ ±10= ,
REMEMBER THE WORDING!!
We are 95% confident that the interval from _______ to _______ captures the actual value of the mean final exam score.
context
confident
We don’t say 95% chance or probability of capturing the actual value of the parameter because the interval either does (prob = 1) or doesn’t capture it (prob = 0).

6. The confidence level 𝐶 tells us how likely it is that the method we are using will produce an interval that captures the population parameter if we use it many times.
Doesn’t tell us the chance that a particular interval captures the parameter.
A confidence interval gives a set of plausible values for the parameter.
If we were to repeat the sampling procedure many times, about 95% of the confidence intervals computed would capture the mean final exam score.
𝑥 = ____
_____ ± 10= ,
𝑥 = ____
_____ ± 10= ,
Use the Java applet to take many many samples of size 4 to make
many many confidence intervals. Draw the picture to the right.

7. How much does the fat content of Brand X hot dogs vary
How much does the fat content of Brand X hot dogs vary? To find out, researchers measured the fat content (in grams) of a random sample of 10 Brand X hot dogs. A 95% confidence interval for the population standard deviation σ is 2.84 to 7.55.
Interpret the confidence interval.
Interpret the confidence level.
True or false: The interval from 2.84 to 7.55 has a 95% chance of containing the actual population standard deviation σ. Justify your answer.
We are 95% confident that the interval from 2.84 to 7.55 g captures the true standard deviation of the fat content of Brand X hot dogs.
If we were to repeat the sampling procedure many times, about 95% of the confidence intervals computed would capture the population standard deviation.
False. The probability is either 1 (if the interval does contain the true st dev) or 0 (if it doesn’t).

8. Shorter interval, lower % hit
Bigger interval, higher % hit
Bigger interval, highest % hit (that you’ll be dealing with)
increases
increasing

9. Estimate ± (crit value)(std dev)
Margin of Error depends on critical value and std dev.
Estimate ± 2 𝜎 𝑥
95% confidence
Estimate ± 3 𝜎 𝑥
99.7% confidence
General Formula:
Estimate ± (crit value)(std dev)
The critical value depends on the confidence level.
We will be calculating different critical values in Ch. 8-2 and 8-3.
What kind of critical values would reduce the margin of error?
lower values
Lower standard deviation by _____________________
increasing sample size
Larger samples give more precise estimates  _______________
less variability
Why don’t we always get large sample sizes in the real world?
Very costly and time-consuming

10. 𝑝 𝜇
random
randomized
normal
the population
distribution is normal OR by the CLT if 𝑛≥30.
𝑛𝑝≥10 and 𝑛 1−𝑝 ≥10
10% condition

11. SRS
stratified
cluster
random sampling
random assignment