Download Chap 14 Lesson 1

Chapter 14: Confidence Intervals: The Basics
The usual reason for taking a sample is not to learn about the individuals in the
sample but to infer from the sample data some conclusion about the wider
population that the sample represents.
Statistical Inference = provides methods for drawing conclusions about a
population from sample data.
 since different samples can lead to different conclusions, we cannot be
completely certain that our conclusions are correct
 inference uses concepts of probability to state how trustworthy our
conclusions are
 the two most common types of inference are confidence intervals and
tests of significance
We are going to start with confidence intervals that are used for inference about
a mean.
For now we are going to assume some simple (but unrealistic) conditions:
1. We have a perfect SRS from the population of interest with no
nonresponse or other issues.
2. The population is perfectly Normal with N(µ,σ).
3. We don’t know the population mean µ but we do know the population
standard deviation σ.
These facts will lead us to being able to estimate µ with a certain level of
confidence.
Example 14.1 (page 344)
x
= ___________
σ = ____________
n = ____________
We want to estimate µ for a population of more than 10 million young men of
these ages. We will need to use the facts we previously learned about sampling
distributions:
µ x = __________ and σ x = ___________
However, we know that µ is not going to be exactly the same as x so we will set
up an interval of values that we think µ is in, allowing some room for error.
First, find the standard deviation σ x of the samples: ______________________
We want to estimate the mean for 95% of the sample. Since the population is
Normal, we know 95% is equivalent to _______ standard deviations from the
mean.
So µ is within _________ of the sample mean, called the margin of error.
Therefore, the mean falls within the interval:
This means that 95% of the samples will give us a mean score between 267.8
and 276.2.
Confidence Interval = used to estimate unknown population parameters by
providing a range of plausible values and attaching a level of certainty to that
range of values.
A level C confidence interval has two parts:
1. An interval calculated from the data by:
point estimate ± margin of error
2. A confidence level C which gives the probability that the interval will
actually capture the true parameter value in repeated samples (= the
success rate).
 experimenters choose C to be any % but usually 90% or above
because you obviously want to be very sure about your conclusions
 most commonly used is 95%
 means “we are 95% confident that µ lies within the interval” which
really means we got these numbers using a method that gives
correct results 95% of the time
For our example, we are 95% confident that the mean test score is between
267.8 and 276.2.
Chapter 14: Confidence Intervals: The Basics
The usual reason for taking a sample is not to learn about the individuals in the
sample but to ____________________________________________________
_______________________________________________________________
Statistical Inference = ____________________________________________
_____________________________________________
 since different samples can lead to different conclusions, we cannot be
completely certain that our conclusions are correct
 inference uses ____________________________________________
_______________________________________
 the two most common types of inference are ____________________
_____________and ______________________________________
We are going to start with confidence intervals that are used for inference about
a mean.
For now we are going to assume some simple (but unrealistic) conditions:
1.
2.
3.
These facts will lead us to being able to estimate µ with a certain level of
confidence.
Example 14.1 (page 344)
x
= ___________
σ = ____________
n = ____________
We want to estimate µ for a population of more than 10 million young men of
these ages. We will need to use the facts we previously learned about sampling
distributions:
µ x = __________ and σ x = ___________
However, we know that µ is not going to be exactly the same as x so we will set
up an interval of values that we think µ is in, allowing some room for error.
First, find the standard deviation σ x of the samples: ______________________
We want to estimate the mean for 95% of the sample. Since the population is
Normal, we know 95% is equivalent to _______ standard deviations from the
mean.
So µ is within _________ of the sample mean, called the _________________.
Therefore, the mean falls within the interval:
This means that __________________________________________________
_______________________________________________.
Confidence Interval =
A level C confidence interval has two parts:
1. An interval calculated from the data by:
2. A confidence level C which gives ________________________________
___________________________________________________________
 experimenters choose C to be any % but usually _______________
because you obviously want to be very sure about your conclusions
 most commonly used is _________
 means “_______________________________________________”
which really means we got these numbers using a method that gives
correct results 95% of the time
For our example, _________________________________________________
________________________________________________.