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Draft curriculum 2006. Statistical inference sampling variability estimate intervals sampling/ non sampling errors parameters estimates sample size effect margins of error variability of an estimate margin of error in the media. - PowerPoint PPT Presentation
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DEPARTMENT OF STATISTICS
Statistical inference sampling variability
estimate intervals sampling/nonsampling errors
parameters estimates sample size effect margins of error variability of an estimate
margin of error in the media
A unit of work prepared and presented by: Marina Mcfarland & Anne Blundell (AGGS)
Matt Regan (Stats Dept)
Draft curriculum 2006
DEPARTMENT OF STATISTICS
Draft curriculum 2006: Statistical investigation (thinking)
Level 6: - making informal inferences about populations from sample data and communicating findings
Level 7: - using sample statistics to make point estimates of population parameters
- recognising the effect of sample size on the variability of an estimate
Level 8: - determining estimates and confidence intervals for mean, proportions and differences
DEPARTMENT OF STATISTICS
Level 7 - identifying sampling and possible non-sampling errors in polls and surveys
Level 8 - . . . interpreting margins of error
Draft curriculum 2006: Statistical investigation (thinking)
DEPARTMENT OF STATISTICS
What proportion of NZ Year 5 -10 pupils (mainly) run around at lunchtime?
Population
Sample (n = 30)
DEPARTMENT OF STATISTICS
What proportion of NZ Year 5 -10 students (mainly) run around at lunch time?
DEPARTMENT OF STATISTICS
What proportion of NZ Year 5 -10 pupils (mainly) run around at lunchtime?
Sample (n = 30)
Population
0.53 or 53%
1. The proportion of pupils in my sample who mainly run around during their lunchtime =
DEPARTMENT OF STATISTICS
2. So, I estimate that about of all Yr 5–10 pupils mainly run around during their lunchtime.
What proportion of NZ Year 5 -10 pupils (mainly) run around at lunchtime?
Sample (n = 30)
Population
0.53 or 53%
DEPARTMENT OF STATISTICS
What proportion of NZ Year 5 -10 pupils (mainly) run around at lunchtime?
What did others in the class get for their estimates?
I notice that:
Everyone seemed to get a different proportion for their sample
There was a huge range of sample proportions
. . .
DEPARTMENT OF STATISTICS
Sampling variability
Sample 1
(n = 30)
0.50 0.4 0.6 0.70.30.20.1 0.8 0.9 1
Sample 2 (n = 30)
Sample 3 (n = 30)
Sample Proportions
DEPARTMENT OF STATISTICS
What proportion of NZ Year 5 -10 students (mainly) run around at lunch time?
DEPARTMENT OF STATISTICS
Sampling variability
Sample 1
(n = 30)
0.50 0.4 0.6 0.70.30.20.1 0.8 0.9 1
Sample 2 (n = 30)
Sample 3 (n = 30)
. . .
Sample Proportions
DEPARTMENT OF STATISTICS
Sampling variability
Sample 1
(n = 30)
0.50 0.4 0.6 0.70.30.20.1 0.8 0.9 1
Sample 2 (n = 30)
Sample 3 (n = 30)
. . .
Sample Proportions
I notice that:Each sample has different peopleThe sample proportions varyThe variability in the sample proportions
is large
DEPARTMENT OF STATISTICS
Sampling variability
Sample 1
(n = 30)
0.50 0.4 0.6 0.70.30.20.1 0.8 0.9 1
Sample 2 (n = 30)
Sample 3 (n = 30)
. . .
Sample Proportions
It is a fairly safe bet that:• any sample proportion will be no further than
20% away from the population proportion
≈ 20%
DEPARTMENT OF STATISTICS
Sampling variability
Sample 1
(n = 30)
0.50 0.4 0.6 0.70.30.20.1 0.8 0.9 1
Sample 2 (n = 30)
Sample 3 (n = 30)
. . .
Sample Proportions
It is a fairly safe bet that:• the population proportion will be no further than
20% away from any sample proportion
≈ 20%
DEPARTMENT OF STATISTICS
What proportion of NZ Year 5 -10 pupils (mainly) run around at lunchtime?
Sample (n = 30)
Population
0.53 or 53%
1. The proportion of pupils in my sample who mainly run around during their lunchtime =
DEPARTMENT OF STATISTICS
What proportion of NZ Year 5 -10 pupils (mainly) run around at lunchtime?
I notice that:This range of possible values for the population proportion is so wide that it is practically useless.
3. It’s a fairly safe bet that the proportion of all Yr 5–10 pupils who mainly run around during their lunchtime (i.e., the population proportion) is:
• no further than 20% away from my sample proportion of 53%
• somewhere between 33% and 73%
• 53% with a margin of error of 20%
DEPARTMENT OF STATISTICS
Different sample sizes
0.50 0.4 0.6 0.70.30.20.1 0.8 0.9 1
Sample 1 (n = 100)
. . .
Sample Proportions
Sample 2 (n = 100)
DEPARTMENT OF STATISTICS
DEPARTMENT OF STATISTICS
n = 100
0.50.45 0.55 0.60.40.350.3 0.65 0.7Sample Proportions
I notice that:
It is a fairly safe bet that the population proportion will be no further than 9% away from any sample proportion.
(Note: )
≈ 9%
%101.01001
Different sample sizes
DEPARTMENT OF STATISTICS
Different sample sizes
0.50 0.4 0.6 0.70.30.20.1 0.8 0.9 1
Sample 1 (n = 250)
. . .
Sample Proportions
Sample 2 (n = 250)
DEPARTMENT OF STATISTICS
DEPARTMENT OF STATISTICS
Different sample sizes
n = 250
0.50.45 0.55 0.60.40.350.3 0.65 0.7Sample Proportions
I notice that:
It is a fairly safe bet that the population proportion will be no further than 6% away from any sample proportion.
(Note: )
≈ 6%
%606.02501
DEPARTMENT OF STATISTICS
Different sample sizes
n = 1000
0.50.45 0.55 0.60.40.350.3 0.65 0.7Sample Proportions
I notice that:
It is a fairly safe bet that the population proportion will be no further than 4% away from any sample proportion.
(Note: )
≈ 4%
%303.010001
DEPARTMENT OF STATISTICS
Conclusion:
It is a fairly safe bet that for a random sample of size n, the population proportion will be no further than from the sample proportion.n1
What proportion of NZ Year 5 -10 pupils (mainly) run around at lunchtime?
DEPARTMENT OF STATISTICS
4. When I use a sample proportion to estimate a population proportion then I should use a sample size, n, of at least:
• n = 250 if I want my sample proportion to be no further than about 0.06 or 6% (= ) away from the population proportion
2501
• n = 1000 if I want my sample proportion to be no further than about 0.03 or 3% (= ) away from the population proportion
10001
What proportion of NZ Year 5 -10 pupils (mainly) run around at lunchtime?
DEPARTMENT OF STATISTICS
5. Randomly select a sample of size n = 1000 pupils from the population of all Yr 5–10 pupils:
What proportion of NZ Year 5 -10 pupils (mainly) run around at lunchtime?
DEPARTMENT OF STATISTICS
DEPARTMENT OF STATISTICS
It’s a fairly safe bet that between 48% and 54% of all Yr 5–10 pupils mainly run around in their lunchtime.
5. Randomly select a sample of size n = 1000 pupils from the population of all Yr 5–10 pupils:
• My sample proportion = 0.51 or 51%
• With 1000 pupils in my sample, it is a fairly safe bet that my sample proportion is no further than 0.03 or 3% away from the population proportion.
What proportion of NZ Year 5 -10 pupils (mainly) run around at lunchtime?
DEPARTMENT OF STATISTICS
What proportion of NZ Year 5 -10 pupils (mainly) run around at lunchtime?
• Summary
• Warning
• Exercise
DEPARTMENT OF STATISTICS
• Sampling / nonsampling errors
• ‘Random sample’ versus ‘simple random sample’
• Population size and the margin of error
• Is ‘n = 30’ sufficiently large to satisfy underlying theory?
Some issues