Today:
- Statistics in the news: "Statistics the Weapon of Choice in Surge Debate"
- Return Quiz 4
- Quiz 5 - normals and z-scores
- Chapter 4, sections 1-4: the normal distribution
- Using the Z-table backwards:
- Section 4.5: using the normal to make inferences
- Someone makes a claim: does it make sense? How can we tell?
-
- A common rule:
- If the probability of an observed sample is .05 or less
(that is, a 1 in 20 chance of worse), assuming the truth of some conjecture,
then the sample is contradictory to that conjecture. Otherwise the sample will
not be considered contradictory to the conjecture.
- Strategy: Inference making procedure, p. 136
- Example: #3, p. 137
- Section 5.1: Sampling distributions and the normal curve (why is the
normal distribution so important?)
- A statistic is a number that we calculate from a
sample of data:
- A parameter is a number that could be calculated
from a population if all of the data were accessible:
- Generally we pull many values from a population to form a
sample.
- It turns out that if we take relatively large samples, sample
after sample, and compute the statistic over and over, the histogram of
statistic values will look bell-shaped.
- The sampling distribution of the mean
- Properties of the sampling distribution:
- The mean of the sampling distribution of the sample mean
, denoted
, is equal to the mean of the population
.
- The standard deviation of the sampling distribution of the sample mean
, denoted
, is
where n is the sample size. This statistic is called the
standard error of the mean, and you will see it
reported by StatCrunch, for example.
- Here's the key thing: the sampling distribution is approximately normal for a large sample size n ("large" generally taken as greater than or equal to n=30).
- See Figure 5.5, p. 172
- This result is encapsulated in The Central Limit Theorem
(p. 167), and in the graphs of Figure 5.3, p. 168.
- Calculating probabilities for sample means involves computing
Z-scores, as we've done in the past: see p. 171.
- Example problem: #4, p. 177
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