Chapter 8
Estimating with Confidence
Definitions
 A point estimator is a statistic that provides an estimate of a
population parameter. The value of that statistic from a
sample is call a point estimate.
 Ideally, a point estimate is our “best guess” at the value of an
unknown parameter.
 Example: Tonya wants to estimate what proportion of
students are going to attend the prom. She interviews a SRS
of 50 of the 750 students at her school and finds that 36 of
them are going to the prom. What is the point estimator?
Confidence Interval
To say that we are 95%
confident is shorthand for
“95% of all possible
samples of a given size
from this population will
result in an interval that
captures the unknown
parameter.”
Confidence Intervals
In general:
confidence interval = estimate ± margin of error
When calculating:
confidence interval = statistic ± (critical value)(std dev of statistic)
“We are C% confident that the interval ___ to ___ captures the actual
value of the [population parameter in context].”
Conditions
 Conditions for constructing confidence interval:
 Random
 Normal
 Independent – Individual observations are independent.
(sample size n should be no more that 10% of the pop)
8.2 Proportions
 Confidence interval for p:
𝑝 ± 𝑧∗
𝑝(1−𝑝)
𝑛
 Ex: Mrs. Ramsey’s class took a SRS of beads from a container
and got 107 red beads and 144 white beads. Calculate and
interpret a 90% confidence interval for p.
Keep going…
 So z* for our problem is _____
 Confidence interval:
Sample Sizes
 To determine a sample size n that will give you a
certain confidence interval, you use:

𝑧∗
𝑝(1−𝑝)
𝑛
≤ 𝑀𝐸
Example
 Determine the sample size needed to estimate p
within 0.03 with 95% confidence.
Homework
 Pg. 481 (16, 17, 21-24)
 Pg. 496 (27-33, 40, 42, 44-47, 49-52)