Summary
2.2C International Bachelor of Psychology Statistics II summary
- Course
- Institution
In depth summary of bookchapters, study material and lectures of second year Statistics course. I got a 9.6 for the exam.
[Show more]
Seller
Follow
gg12121
Reviews received
Content preview
MMC Chapter 8: Proportions➔ Binomial distribution review from 1.3
◆ Conditions:
● Fixed number of observations n
● n observations are all independent
● Each observation falls into one of the two categories “success” or
“failure”
● Probability of success (p) is the same for all observations
◆ Examples: coin toss, yes/no survey
◆ B(n,p)
◆ Binomial distributions are important when we want to make inferences about
the proportion p of successes in a population
◆ Generally, we use binomial sampling distribution for counts when the population
is at least 20 times as large as the sample
◆ If a count X has the binomial distribution B(n,p), then:
◆ the count X has a binomial distribution, not the p^ !!
_____________
8.1 Inference for a single proportion
➔ we record counts or proportions when we collect data about a categorical variable from
a population
➔ we draw a simple random sample (SRS) from the population
➔ the sample proportion p^= X/n estimates the unknown population proportion p
➔ if the population is at least 20 times as large as the sample, then the count X has a
binomial distribution B(n,p)
➔ When the sample size n sufficiently large, the sampling distribution of p^ is
approximately normal with mean and standard deviation
,➔ however, we don’t know the population proportion p, so we have to replace it with p^---
now it’s called standard error
➔ We use the large-sample confidence interval for 90%, 95%, and 99% confidence
whenever the number of successes and the number of failures are both at least 10.
➔ For smaller sample sizes, we recommend exact methods that use the binomial
distribution.
➔ There is also an intermediate case between large samples and very small samples where
a slight modification of the large-sample approach works quite well. This method is
called the “plus four” procedure:
➔ We add 4 observations to the sample, with 2 successes and 2 failures
➔ Significance test for a single proportion:
◆ distribution of sample proportion p^ is appx. normal— to construct confidence
intervals, we substitute p^ in place of pto obtain the standard error (and use it
for margin or error)
◆ however in significance testing, we assume that the value given by null
hypothesis for p is true H0: p=p0
, ◆
◆ In problems like which product is better etc., two-died tests should be used
because we cannot make a scientific claim on the superiority of one product over
another (for advertising purposes etc.)
◆ we often don’t conduct sig tests for a single proportion because there is often
not a single p0 we want to test— i.g. coin tossing, drawing cards, proportions
from previous studies etc. could provide p0
➔ choosing a sample size for confidence interval:
◆
◆ we aim to pick a specific sample size for our desired margin of error
◆ chosen confidence level determines the z-value
◆ we don’t know p^ yet bc we didn’t collect data yet:
● we can use p^ from a previous similar study
● we can take p^=0.5, because the margin of error is largest in this case and
it will generate n larger than we actually need (safe choice)
◆ then, we can calculate n
, 8.2 Comparing two proportions
➔ now we compare two proportions from 2 populations
➔ the difference between 2 sample proportions: D=p^1-p^2
➔ when both sample sizes are large, sampling distribution of the difference D is appx
normal
➔ mean of D: (addition rule for means)
➔ standard deviation of D:
➔ Confidence interval for a difference in proportions:
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 gg12121. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $14.45. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
82956 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy study notes for 14 years now