77 students were asked to choose 3 of the integers 11, 12 ,13, · · ·, 30 completely arbitrarily. The amazing result was as follows.

If the selection were completely random, the following hypotheses should be true.(a) The 20 numbers are equally likely.

(a) The 20 numbers are equally likely.

(b) The 10 even numbers together are as likely as the 10 odd numbers together.

(c) The 6 prime numbers together have probability 0.3 and the 14 other numbers together have probability 0.7. Test these hypotheses, using α = 5%. Design further experiments that illustrate the difficulties of random selection.

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Number 11 12 13 14 15 16 17 18 19 20 11 10 20 8 13 9 21 Number 21 22 23 24 25 26 27 28 29 30 9 16 8 Frequ. 8 15 10 10 8 13 Frequ. 12 9 12