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Understanding Informal Confidence Intervals in Statistical Analysis

Explore the relationship between IQRs for sample medians, population IQRs, and sample sizes to determine the ideal interval for population medians. Learn to calculate confidence intervals and make statistical inferences using practical examples.

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Understanding Informal Confidence Intervals in Statistical Analysis

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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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