1. From Samples to Populations
Chapter 8
From Samples to Populations

2. Sampling Distributions
The distribution of sample means is the distribution that results when we find the means of all possible samples of a given size. The larger the sample size, the more closely this distribution approximates a normal distribution. In all cases, the mean of the distribution of sample means equals the population mean. If only one sample is available, its sample mean is the best estimate for the population mean, µ. (Chapter 5 p209, Central Limit Theorem)
GED111/CDS111 Statistics in Modern Society

3. GED111/CDS111 Statistics in Modern Society
Sampling Error
The error that is introduced when a random sample is used to estimate a population parameter is called a sampling error. It does NOT include other sources of error, such as those due to biased sampling, bad survey questions, or recording mistakes.
A practical way to reduce the sampling error would be to increase the sample size, n.
GED111/CDS111 Statistics in Modern Society

4. GED111/CDS111 Statistics in Modern Society
Exercise
Q5-8 p343
GED111/CDS111 Statistics in Modern Society

5. Estimating Population Means
Point estimate
Sample mean
Interval Estimate
Confidence Interval
95% confidence interval for a population mean
Margin of error, E, ≈ 2s/√n
S is the standard deviation of the sample
n is the sample size
GED111/CDS111 Statistics in Modern Society

6. 95% confidence interval for a population mean
From (sample mean – margin of error) to (sample mean + margin of error)
Sample mean – E < µ < sample mean + E Or
Sample mean ± E
Figure 8.10 p348
GED111/CDS111 Statistics in Modern Society

7. Choosing Sample Size to estimate µ
n = (2σ/E)2
σ is the population standard deviation (usually estimated)
Margin of error, E, is often known in advance (being specified)
GED111/CDS111 Statistics in Modern Society

8. GED111/CDS111 Statistics in Modern Society
Exercise
Q5-8 p353
GED111/CDS111 Statistics in Modern Society

9. 95% confidence interval for a population proportion
E ≈ 2√((p(1-p)/n)
p is the sample proportion
n is the sample size
From p – margin of error to p + margin of error
p – E < P < p + E ^ ^ ^ ^ ^ ^ ^
GED111/CDS111 Statistics in Modern Society

10. Choosing Sample Size to estimate P
At least
n = 1/E2
Any sample size equal to or larger than this value will suffice
GED111/CDS111 Statistics in Modern Society

11. GED111/CDS111 Statistics in Modern Society
Exercise
Q22, 30 p
Focus on Literature
How Many Words Did Shakespeare Know? P
GED111/CDS111 Statistics in Modern Society