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Lecture 5

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University of Guelph

Sociology and Anthropology

SOAN 3120

Scott Schau

Fall

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Quantitative Methods Week 5
SOAN 3120 Oct. 9, 11
Confidence Interval
- A level C confidence interval for a parameter has two parts: an interval calculated from the data,
usually of the form: estimate ± margin of error
- A confidence level C, which gives the probability that the interval will capture the true
parameter value(μ) in repeated samples, or the success rate for the method
Interpreting a confidence interval for a mean
- A confidence level can be expresses as Xbar ±m (m is the margin of error)
- Two endpoints of an interval μ possibly within (xbar – m) to (xbar + m)
- Confidence intervals contain the population mean μ in C% of samples. Different areas under the
curve give different levels C.
Practical use of z: z*
- Z* is related to the chosen confidence level C
- C is the area under the standard normal curve between –z* and z*
- The confidence interval is thus : xbar ± z* ơ/ √n
Link between confidence level and margin of error
- The confidence level C determines the value of z* (in table C). the margin of error also depends
on z*. higher confidence C implies a larger margin f error m, thus less precision in our estimates)
- A lower confidence level C produces a smaller margin of error m, thus better precision in our
estimates
Impact of sample size
- Spread in the sampling dist, of the mean is a function od the number of individuals per sample.
- The larger the sample size the smaller the SD(spread) of the sample mean dist,
- But the spread only decreases at a rate equal to √n
Sample size and experimental design
- You may need a certain margin of error (eg. Drug trial manufacturing specs). In many cases, the
population variability (ơ) is fixed, but we can choose the number of measurements (n).
- So plan ahead what sample size to use to achieve that margin of error
- M= z* ơ/ √n n= (z*ơ/m)²
The reasoning of tests of significance
- Suppose a basketball player claimed to be an 80% free throw shooter. To test his claim, we have
him attempt 50 free throws. He makes 32 of them. His sample proportion of made shots is
32/50 = .64 what can we conclude about the claim based in this sample data? Quantitative Methods

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