Summary
Summary Stats 188 chapter 8 notes
- Course
- Institution
- Book
Summary of stats chapter 8 notes, for second semester
[Show more]
Connected book
Book Title:
Author(s):
- Edition:
- ISBN:
- Edition:
More summaries for
-
Stats 188 chapter 7 notes
1 review
By: eckojvr • 1 year ago
Seller
Follow
juliayates19
Reviews received
Content preview
CHAPTER 8: CONFIDENCE INTERVAL ESTIMATION> CHARACTERISTICS OF ESTIMATORS :
◦ unbiased ness :
expectation of the estimator equals the parameter value .
◦
Consistency : Unbiased estimator that approaches population values as sample size increases .
Efficiency Unbiased estimator that has minimal standard error
◦ : .
> A confidence interval estimate = a
range of numbers ,
called an interval ,
constructed around the point estimate
GENERAL FORMULA : A point estimate is the
value of a single sample
Point Estimate ± ( critical value ) ( standard Error ) statistic ,
such as the mean
,
CONFIDENCE INTERVAL ESTIMATE FOR THE MEAN 10 Known )
◦ ASSUMPTIONS :
population standard deviation 0 IS known
population is
normally distributed
If population is not normal ,
use large sample In 30 )
CONFIDENCE INTERVAL ESTIMATE :
-
± Za, , O : point estimate
n
✗
12
: the normal distribution critical Value for a
probability Of ✗ 12 In each tail
" " " "" " ""
EXAMPLE used
:
commonly confidence
◦
1 Consider a 95.1 .
confidence interval : £42 = I 1.96 intervals are : 90 1.
-
,
95 1
'
.
I ✗ 0.95 ✗ and 99.1
'
-
= . . = 0.05 .
'0
I >
↑
a
2=0 =
0.025
.
V
ZX / 2=-1.96 O ZX / 2=1.96
2- units :
✗ Units : Lower confidence point upper confidence
Limit Estimate Limit
, >
SAMPLING ERROR :
sampling due single sample from the population
•
is the variation
error that occurs to
selecting a .
>
The size of the sampling error =
primarily based on the amount of variation in the population and on the
sample size .
>
Large samples have less large to select
sampling error than small samples , but samples cost more .
* The value of 2- ✗ 12 needed to construct a confidence interval is called the critical value for the distribution
CONFIDENCE INTERVAL ESTIMATE FOR THE MEAN 10 unknown )
o If the population standard deviation 0 Is unknown
,
we can substitute the sample standard deviation ,
S
1 This introduces an extra uncertainty ,
since S Is a variable from sample to sample .
> distribution normal distribution
'
. . Use the t instead Of the
o ASSUMPTIONS :
population standard deviation is unknown
population is normally distributed
CONFIDENCE INTERVAL ESTIMATE i
s
t ✗ 12
-
n
>
STUDENT 'S T DISTRIBUTION NOTE : t > 2- as n increases
• The tan value depends on degrees of freedom Idf )
df = n -
l standard normal
fi)
Lumber Of Observations that are free to (t with df =
X )
vary after sample mean has been calculated
no , ,},
g.) [ tldf
(
= 5)
t
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller juliayates19. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $4.79. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
81989 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy study notes for 14 years now