1. Inference 91264 4 credits Making the call……..
Use a topical example in the media to introduce the idea of sampling: eg campbell live, nzherald, facebook
Leads discussion
How well do the views expressed reflect the views of all NZers? Why not?
How could we gather views of all NZers? Census, but this is time consuming and expensive (NB some countries are considering doing away with the census because of high (10%) non-response.)
We take a sample (eg blood sample)
Click on the dot for link to science project

2. Standard Clarifications Help Achievement objectives
Click standard and clarifications for links
Click on help for link to Nayland
Clarifications
Achievement objectives
Help

3. P It is written in the form of a question?
It can be answered with the data supplied.
The parameter is stated (median).
The population of interest is clear.
The variables of interest are specified.
The intent is clear (comparison).
One that is interesting: is the answer useful? P
roblem
Click dot for link to inference questions power point
pose an appropriate comparison,
investigative question from a given set of population data
Writing your question……..

4. P Source of data. State your hypothesis.
Justification for the random sampling method.
Will be representative of the population.
Select your sample size provide justification.
Tools used for taking your sample (Nzgrapher) P
lan
Click dot for basics in inference kahoot – need to log in to kahoot first
Writing your plan……..

5. D State variables and units of measurement.
Present table of sample data selected.
ata
Click dot for nz grapher
Take a random sample…

6. D Purpose of taking a sample
To make an estimate of what is going on back in the population D
ata
Click dot for
Take a random sample…

7. D Reasons for sampling Time and cost considerations,
lack of access to the entire population and the nature of the data collection or test, For example, blood test does not require all blood to be taken D
ata
Click dot for
Take a random sample…

8. D Features of a good sample,
One that represents, it is representative of the population
The sample size is sufficiently large; if a sample is too small, it is more likely to be unusual and less likely to be representative. D
ata
Click dot for nz grapher
Take a random sample…

9. D Features of a good sample,
There is no statistical requirement that a sample be a proportion of the population; a well designed sampling process is more likely to produce a representative sample than a large sample poorly selected. D
ata
Click dot for nz grapher
Take a random sample…

10. D Features of a good sample,
Randomly chosen: each member of the population has the same chance of being included in the sample. D
ata
Click dot for taking a random sample
Take a random sample…

11. D Buffon’s Needles Exploration ata Take a random sample…
Click dot for Buffon’s needle
Take a random sample…

12. Symbols for some of the common characteristics
A parameter is any numerical characteristic of a population.
Eg. Population proportion, population mean, population standard deviation
A statistic is a numerical characteristic calculated from a sample
Eg. Sample proportion, sample mean, sample standard deviation
Symbols for some of the common characteristics
Characteristic
Sample statistic symbol
Population parameter symbol
Mean
“mu”
Proportion p
“pi”
Standard deviation s
“sigma”

13. Copy the following, filling in the correct words from the list below
When organisations require………….they either use data collected by somebody else (secondary data), or collect it themselves (primary data).
This is usually done by …………, that is collecting data from a …………….. sample of the …………… they are interested in. If it is of any use, the sample must represent the whole population we are interested in and not be ………… in any way. The point of collecting data is to deduce information about the entire population, this is called making ………….
data
representative
sampling
population
biased
inferences
Sampling inferences data
Population representative biased

15. D
Data

16. Take your samples and draw your plots

17. A
nalysis

18. BLAH
BLAH NO
BLAH
BLAH
BLAH
BLAH
BLAH

19. Box Plots
Discuss these groupings   - Shape - Unusual aspects
- Centre (middle 50%, median)
- Shift / Overlap (distance between medians)
‘I notice ...  I expected ...  I was surprised that...’ Also consider possible reasons or causes of these features (in the context)

20. Be clear and concise
Give relevant information
Supporting evidence
Link to research

21. C

22. Sampling Error
The process of taking a sample and using the median of the sample to predict the population median will never produce the exact value of the population median. This is called sampling error, the difference between the sample median and the true value back in the population.

23. Sampling variability:
– effect of spread in population
We can cope with the uncertainty of predicting the population median by giving a possible range of values, an interval within which the population parameter probably lies.

24. Informal confidence interval for the median
Note that as sample size increases from 100 to 400, times 4, the range of possible values of the median decreases to half the size
(there is an inverse relationship based on square root)

25. Informal confidence interval for the median
Our best measure of spread is given by using the IQR of the sample as an estimate of the IQR of the population.
This is more consistent than the range which is affected by outliers.

26. Informal confidence interval for the median
The formula for the range of values
is inversely proportional to sample size (n)
depends on the variation within the sample.
 Population median = sample median ± 1.5 IQR ÷ √n

27. Informal confidence interval for the median
The confidence intervals are narrower for a larger sample size.
Simulation shows that the interval includes the true population median for 9 out of 10 samples

28. Making a claim based on informal confidence intervals for the median, comparing two populations.  
If the blue intervals do not overlap we have sufficient evidence to claim that a difference exists back in the population.
If the blue intervals overlap we cannot say which group values are bigger back in the population. The shift may even be the other way round to what is shown in the box plot.

29. C onclusion Use your confidence intervals Make a claim using
the medians
Click dot for description of confidence interval
on the population
Answer your question

30. WE
NEED TO
Evaluate
The first rule is: Treat your audience as king.

31. 2
the
process
The second rule is: Spread ideas and move people.

32. 3
THE
conclusion
The next rule is: Help them see what you are saying.

33. 4
the
research
IT’S supportive
or not

34. 5 CONNECT CONFIDENCE CULTIVATE
The last rule is: Cultivate healthy relationships (with your slides and your audience)

35. And practice, practice, practice.

36. Quantification of the conclusion
The median height and mean height for the boys was 170 cm compared with the median height and mean height for girls of 164 cm. This suggests that boys are on average about 6 cm taller than girls in Grade 10. There is a small amount of overlap between the middle 50% of height values. This small overlap supports the conclusion that boys are on average taller than girls. Also 75% of the boys are taller than 50% of the girls.
Generalisation
The findings of this investigation suggest that boys are taller than girls in Grade 10. These findings could be applied to the Grade 10 population in general in Qatar. It would appear to be true for these data.
And practice, practice, practice.