Summary
Confidence Interval for a Proportion - Summary
- Course
- Institution
Summary of the Confidence Interval for a Proportion
[Show more]
Seller
Follow
amywillis
Content preview
STA1003: Fundamental StatisticsConfidence Interval for a Proportion
Overview:
What is meant by a confidence interval;
How to calculate a confidence interval for a proportion;
What is meant by a 90%, 95%, 98% or 99% confidence interval;
How to find a sample size;
Margin of error.
Introduction:
So far, we have taken samples from a known population
Usually the details about the population are unknown
So (for example) µ and p are unknown
In general, we take a sample to find out about the unknown population to
draw conclusions about parameters (inference)
Samples and populations:
Statistics are numbers describing samples
Parameters are numbers describing populations
Usually, Roman letters denote statistics (eg. y, s)
Usually, Greek letters denote parameters (eg. µ, σ)
Each statistic has an associated parameter
Parameters are usually unknown, and estimated by statistics
For Example…
To estimate the population mean, use the sample mean
But different samples will produce different sample means y, and hence
different estimates of µ
How confident are we in our estimate of µ?
(We’d be more confident in results from larger samples)
We can construct a confidence interval for µ
To estimate the population proportion, use the sample proportion
But different samples will produce different sample proportions pb, and
hence different estimates of p
How confident are we in our estimate of p?
(We’d be more confident in results from larger samples)
We can construct a confidence interval for p
, STA1003: Fundamental Statistics
Recall:
Because the sampling distribution of pb has a Normal model. . .
. . . we can use the 68–95–99.7 rule:
o 68% of the sample proportions are within one SE of p
o 95% of the sample proportions are within two SE of p
o 99.7% of the sample proportions are within three SE of p
Sample proportions:
Think from the p point-of-view
Confidence intervals:
A typical confidence interval looks like this:
The 95% confidence interval for p is from 0.25 to 0.35
or simply (0.25, 0.35).
Or we write it like this:
The 95% confidence interval for p is 0.30 ± 0.05
The ‘±’ means ‘plus and minus’, so it means
Lower limit = 0.30 − 0.05 = 0.25
Upper limit = 0.30 + 0.05 = 0.35
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 amywillis. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $7.99. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
75759 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy study notes for 14 years now