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Kiwi kapers 3

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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Kiwi kapers 3

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  1. Kiwi kapers 3

  2. 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

  3. 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

  4. 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.

  5. 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

  6. 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)

  7. 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

  8. 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

  9. 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

  10. 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

  11. Final formula for informal Confidence interval The final formula for the informal confidence interval is :

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