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Lecture 4

# SOCY211 Week 4, Lecture 2

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Queen's University

Sociology

SOCY 211

Carl Keane

Winter

Description

Z-Scores and the Normal Curve
- Using examples from the SOCY211 test 1
- Mean: 30/40= 75% Standard Deviation (s)= 5
- 68% of the class will fall within one standard deviation below the mean of 30 and one
standard deviation above the mean of 30 (between 25-35 out of 40—62.5%-87.5%)
- We can compute Z scores: i.e., 15 students scored 32/40= 80%
- Z score for 32= ̅
- From z score to the mean= 0.1554 Area beyond the z score= 0.3446
- Calculation of the percentage of people that they did better than (people with a score of
32)= 0.1554 + 0.5 (other side of the mean)= 0.655 = 65%
- Score that is above the mean has a positive z score; below the mean, negative z score
- Example: 25/40= 62.5%
- Area to the mean- 0.3413 Area beyond z score- 0.1587
- Students that scored 25/40 did better than 15.9% of the class
- If we add the area between their z scores and the mean (0.3413) to the area above the
mean (0.5) we get 0.8413; therefore 84% of the class scored better than students who
scored 25/40
Inferential Statistics
- Refers to a process whereby researchers are able to make inferences about a population
based on results from the sample
o Ex. Public opinion polls do this
- Instead of asking the population we draw a sample (subset) of people from the population
- If we want to learn the population parameters our sample needs to be representative of
the population from which the sample is drawn
- Most basic technique that is used: simple random sampling
o It’s like a lottery—random selection
- Everyone has an equal chance of being selected
- This is achieved through the EPSEM (Equal probability of selection method)
- Allows us to assume that our sample is representative of the larger population and then
we can generalize our results from the sample to the population
- We are interested in how are our results reflective
- There are three concepts:
o 1. Sampling distribution
o 2. Central limit theorem
o 3. Confidence intervals
- We are

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