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Kiwi kapers 3. Relationship between the width of the IQR for sample medians of sample size n and the population IR and the sample size…. IQR for sample medians (sample size = n) is approximately of the population IQR.

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Presentation Transcript
slide2
Relationship between the width of the IQR for sample medians of sample size n and the population IR and the sample size…
  • IQR for sample medians (sample size = n) is approximately of the population IQR
developing an informal confidence interval for the population median
Developing an informal confidence interval for the population median…
  • 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
slide4

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.
slide5

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

that is
That is…
  • 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)

worksheet 2 deciding how many sample iqr n we need for the informal confidence interval finding k
Worksheet 2Deciding how many sample IQR/n we need for the informal confidence interval(finding k)

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
slide8

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
slide9

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

slide10

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

final formula for informal confidence interval
Final formula for informal Confidence interval

The final formula for the informal confidence interval is :

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