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Kiwi kapers 3

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- IQR for sample medians (sample size = n) is approximately of the population IQR

- For our informal confidence interval for the population median we want to use
- Sample median
- Sample IQR/n

- We need to see how big to make this interval so we’re pretty sure the interval includes the population median
- We want it to work about 90% of the time

- Remember we’re in TEACHING WORLD
- We’re going to explore how wide our intervals should be when we can work backwards from a given population.

- Informal confidence intervals…
sample median k x sample IQR/n

- What would be the ideal number (k) of sample IQR/ n to use all the time to be pretty sure the interval includes the population median?

3 different samples n = 30

3 different medians

3 different IQRs

- We know what the population median actually is
- We can look and see how far away from the population median this is:
sample IQR/sqrt(n)

For each example…

- Mark the sample median on the big graph and draw a line to the population median
- Find the distance the sample median is from the population median (2.529kg)
- Divide by sample IQR/n
- This gives the number of sample IQR /n that the sample median is away from the population median
- THIS IS THE NUMBER WE ARE INTERESTED IN

- Mark the sample median on the big graph and draw a line to the population median
- Find the distance the sample median is from the population median (2.529kg)
- Divide by sample IQR/n

EG 4) 0.1222

EG 5) 1.0399

EG 6) 1.0005

EG 7) 1.3007

EG 8) 2.2880

EG 9) 1.3370

EG 10) 1.4119

0.113

0.113/0.12689

= 0.89

3. Divide by sample IQR/n

This gives the number of sample IQR/n that the sample median is away from the population median

0.159

0.159/0.1075

= 1.479

0.212

0.212/0.1479

= 1.433

From our 10 samples it would appear ±1.5 x IQR/sqrt(n) would be most effective.

That is… it should capture the population median most of the time

0.113

0.113/0.12689

= 0.89

3. Divide by sample IQR/n

This gives the number of sample IQR/n that the sample median is away from the population median

0.159

0.159/0.1075

= 1.479

0.212

0.212/0.1479

= 1.433

The final formula for the informal confidence interval is :