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Material Type: Notes; Class: Introduction to Statistics; Subject: Statistics; University: University of California - Berkeley; Term: Unknown 1989;
Typology: Study notes
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From yesterday's USA Today/Gallup Poll โObama was ahead 47%-44% among registered voters, down from a 6-percentage point lead he had last month. McCain led 49%-45% among likely voters, reversing a 5-point Obama lead among that group. In both cases, the margin of error is +/-4 points.โ
From yesterday's USA Today/Gallup Poll โTo determine whether they were likely voters, poll participants were asked how much thought they had given the election, how often they voted in the past and whether they plan to vote this fall... there was an even number of likely voters from each party.โ
Lecture 26:
Recall: population and samples โ We find the statistic(s) of a sample so that we can estimate the parameter(s) of the population โ Unless you perform a census of the whole population, there will always be some chance error, since the sample is only part of the population
Recall: drawing with replacement โ EV of percentage is box percentage โ SE of percentage is โ If n is large, distribution of percentage will be approx. normal
p ๎ 1 โ p ๎ n ร 100 %
Recall: drawing without replacement โ EV of percentage is box percentage โ SE of percentage is โ If n is large (but not close to pop size), distribution of percentage will be approx. normal
p ๎ 1 โ p ๎ n ร
popsize โ samplesize popsize โ 1 ร 100 %
Today โ Yesterday: going from populations to samples โ Today: going from samples to populations
Why everything we looked at yesterday doesn't work
The question โ We take a sample, and find that some percentage of that sample has a certain characteristic โ What does this tell us about the population?
The idea โ For a large, unbiased sample, the sample percentage should be close to the population percentage โ The typical difference between the sample and population percentages is just its standard error โ How do we estimate the standard error if we don't know the box?
The equation โ In that case, we can still use the equation for the SE: except we let p be the sample proportion instead of the population proportion
p ๎ 1 โ p ๎ n ร
popsize โ samplesize popsize โ 1 ร 100 %
Example โ I survey a simple random sample of 1500 Berkeley students (size of population = 34953), and find 25% of the sample watch Hannah Montana โ What can I say about the percentage of all Berkeley students who watch Hannah Montana?
Confidence intervals
The Central Limit Theorem, again โ We know that if the sample size is large and the population is much larger, the sample percentage has an approximately normal distribution โ So we can estimate how large the chance error is likely to be
