Question

Suppose you are asked to estimate the 1st quartile (25% point) from a distribution. You are given a sample of size 30: 7.34 8.16 8.69 8.80 8.82 9.28 9.29 9.38 9.43 9.51 9.65 9.78 9.84 9.95 9.98 9.99 10.02 10.05 10.37 10.42 10.52 10.67 10.78 10.87 11.05 11.12 11.19 11.37 11.54 11.92 Given sorted here.

A. If I just tell you the data is an iid (independent and identically distributed) sample from a distribution, reasoning based on the confidence intervals we construct for the median, what probability distribution with what parameters should I base the confidence interval on? (Use binomial, you figure out n and p)

B. Construct an approximate 80% confidence interval for the lower quartile (the 25% point) (I'm giving you the cumulative distribution from the above, just use it to get 80% of the probability in the interval

0 0.0001785821

1 0.0019644030

2 0.0105958707

3 0.0374493257

4 0.0978695996

5 0.2025980742

6 0.3480542890

7 0.5142899631

8 0.6735991507

9 0.8034066369

10 0.8942718773

11 0.9493417199

12 0.9784063591

13 0.9918208080

14 0.9972504658

15 0.9991810109

16 0.9997843062

17 0.9999499167

18 0.9999897858

19 0.9999981794

20 0.9999997182

21 0.9999999624

22 0.9999999957

23 0.9999999996

24 1.0000000000

25 1.0000000000

26 1.0000000000

Please don't copy any other's answer because they were all wrong. Thank for your help.

Answer 1

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