Class Notes (807,637)
SOAN 3120 (35)
Lecture 5

# quant week 5.docx

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School
University of Guelph
Department
Sociology and Anthropology
Course
SOAN 3120
Professor
Scott Schau
Semester
Fall

Description
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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