STAT10x9.15.05TowardProbability

STAT10x9.15.05TowardProbability - Toward Statistical...

Info iconThis preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon
Toward Statistical Inference Thanks to Joe Chang in the Statistics Department for some lecture content Inference – use information about a sample to draw an inference about the population Example : A CNN/Gallup/USA Today poll of 1000 people reveal that 57% disapprove of Bush’s handling of the Katrina Hurricane disaster. We turn the fact that 57% of the sample have this opinion into an estimate that 57% of all people feel this way. Remember : Parameter – a fixed number that describes a population (i.e., μ = true population mean height). We don’t know this number (Gods only) Statistic – a number that describes a sample (i.e., x = sample mean height). We know this number, but the number can (and usually does) change from sample to sample . Use the statistic to estimate the unknown parameter! Example : MINITAB simulation - - - STAT 101 - 106 Introduction to Statistics 93
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Sampling Variability – If we repeated our sampling procedure ‘many’ times, the same way each time, how much would our statistics change from one sample to the next? Sampling Distribution of a statistic – the distribution of values of a sample statistic in all possible samples of the same size from a fixed population. Example : Let p be the true proportion of the population that approves of Bush (the PARAMETER). Suppose a TOTAL of FOUR people live in the U.S. (this is the population) . I.e., just this once, we know the entire population. Here are their opinions (known to Gods, who are letting us know just this once . . . ) We want to estimate p using a STATISTIC p ˆ , the sample proportion that approves of Bush. In this population, p =0.5 (the parameter, i.e. the true proportion of the population that approves of Bush). STAT 101 - 106 Introduction to Statistics 94 Individua l Attitude 1 Approve 2 Approve 3 Disapprov e 4 Disapprov e
Background image of page 2
NOW : Pretend we don’t know p =0.5, so we take a sample of size n =2. List all possible Simple Random Samples (SRS) of size 2 from this population, and record the sample proportion for each sample (the statistic , p ˆ ) POPULATION POSSIBLE SAMPLES In terms of probability, this is the sampling distribution for p ˆ for samples of size two : STAT 101 - 106 Introduction to Statistics 95 Individua l Attitude 1 Approve 2 Approve 3 Disapprov e 4 Disapprov e Individual s in SRS Attitude p ˆ 1 2 Dis Dis 0 1 3 App Dis 0.5 1 4 App Dis 0.5 2 3 App Dis 0.5 2 4 App Dis 0.5 3 4 App App 1 0 0.5 1 1/6 4/6 1/6
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
The sampling distribution gives All possible values of p ˆ The proportion of times p ˆ takes on each of these values Now : what is the average value of the sample proportion, p ˆ ?. This is called the Mean of a sampling distribution. Mean of a sampling distribution = balancing point In this case, the Mean of sampling distribution of p ˆ = 0.5 This is also the value of the parameter p , the true proportion of the population that approves of Bush. If the mean of the sampling distribution of a statistic equals
Background image of page 4
Image of page 5
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 04/07/2008 for the course STAT 102 taught by Professor Jonathanreuning-schererdonaldgreen during the Fall '05 term at Yale.

Page1 / 28

STAT10x9.15.05TowardProbability - Toward Statistical...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online