# SOC201H1 Lecture Notes - Central Limit Theorem, Statistic, Sampling Distribution

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Chapter 7

February-25-13

11:07 PM

INTRODUCTION

Sampling distributions allow us to refine the estimates provided by statistics calculated on a

sample

POINT ESTIMATES

Sampling error: difference between the calculated value of a sample statistic and the true value of

a population parameter

Point estimate: a statistic provided without indicating a range of error

There is a variability in statistical outcomes from sample to sample

PREDICTING SAMPLE ERRORS

Repeated sampling: drawing a sample and computing its statistics and then drawing a second

sample, a third, a fourth, and so on

English letters used for sample statistics. Greek used for population parameters.

Sampling error is patterned and systematic and therefore is predictable

The resulting sample means were similar in value and tended to cluster around a particular value

o Probability theorists suspected that this value was the true value of the population

parameter

o Sampling variability was mathematically predictable from probability curves

SAMPLING DISTRIBUTIONS

Sampling distribution: from repeated sampling, a mathematical description of all possible

sampling outcomes and the probability of each one

o Eg. The mean age of the population of all doctors is 48 years. Draw 10 000 samples out of

144 doctors. From each sample, calculate the mean age. Plot each value on a histogram and

they will take teh shape of a normal distribution

When the sample size, n, is greater than 121 cases, a sampling distribution of means is normal in

shape.

The mean of a sampling distribution of means will always equal the population mean

o Eg. Sum the values of all 10 000 sample means and divide by 10 000 = 48

A sampling distribution tells us how often a sample statistic is likely to miss the true population

parameter value and by how much

THE STANDARD ERROR

Standard error: the standard deviation of a sampling distribution

o It is a measure of predictable sampling errors

Measures the spread of sampling error that occurs when a population is sampled repeatedly

The standard error of a sampling distribution of means is the sample's standard deviation divided

by teh square root of the sample size n

(I copied and pasted this image from the internet. SEx = s

sfor the variable X

sx = the standard deviation of a sample

## Document Summary

Sampling distributions allow us to refine the estimates provided by statistics calculated on a sample. Sampling error: difference between the calculated value of a sample statistic and the true value of a population parameter. Point estimate: a statistic provided without indicating a range of error. There is a variability in statistical outcomes from sample to sample. Repeated sampling: drawing a sample and computing its statistics and then drawing a second sample, a third, a fourth, and so on. The resulting sample means were similar in value and tended to cluster around a particular value. Sampling error is patterned and systematic and therefore is predictable: probability theorists suspected that this value was the true value of the population parameter, sampling variability was mathematically predictable from probability curves. Sampling distribution: from repeated sampling, a mathematical description of all possible sampling outcomes and the probability of each one: eg. The mean age of the population of all doctors is 48 years.