Kiwi kapers 3
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Transcript of Kiwi kapers 3
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Kiwi kapers 3
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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 n
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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
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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.
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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?
weight
1.5 2.0 2.5 3.0 3.5 4.0
Kiw ipop Dot Plot
3 different samples n = 303 different medians3 different IQRs
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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)
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Worksheet 2Deciding how many sample IQR/n we need for the informal confidence interval(finding k)For each example…1. Mark the sample median on the big graph and
draw a line to the population median2. Find the distance the sample median is from the
population median (2.529kg)3. 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
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1. Mark the sample median on the big graph and draw a line to the population median
2. Find the distance the sample median is from the population median (2.529kg)
3. Divide by sample IQR/n
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EG 4) 0.1222EG 5) 1.0399EG 6) 1.0005EG 7) 1.3007EG 8) 2.2880EG 9) 1.3370EG 10)
1.4119
0.113
0.113/0.12689= 0.89
0.159
0.159/0.1075= 1.479
0.212
0.212/0.1479= 1.433
3. Divide by sample IQR/n
This gives the number of sample IQR/n that the sample median is away from the population median
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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
0.159
0.159/0.1075= 1.479
0.212
0.212/0.1479= 1.433
3. Divide by sample IQR/n
This gives the number of sample IQR/n that the sample median is away from the population median
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The final formula for the informal confidence interval is :
Final formula for informal Confidence interval