Homework #7: Coin Flipping

Due: May 16, 2016 at 14:00.

Read and understand the following instructions on submission of homework. If you do not follow them, you will not receive credit.

Write a plain text e-mail to me. This homework does contain special symbols, but you can copy and paste them from the assignment if you need them and don't know how to input them. (It does not use special wordprocessor features. Do not attach a wordprocessor file such as Microsoft Word or a Excel spreadsheet. I will not read them.) Give the mail the subject "01CN101 Homework #4 by <your name>" in hankaku romaji and send it to math-hw@turnbull.sk.tsukuba.ac.jp. (This subject is helpful for automatically sorting incoming mail.)

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Problems

Problem 1

Suppose you conduct the experiment of flipping a coin 5 times, and counting how many times of 5 "heads" and "tails" appear. Set the null hypothesis H0 as "the coin is unbiased" (also called "fair"). Under H0, compute the distributions of f(heads) and f(tails) ("f(X)" means "count how many times X comes up"). Let P(type II error) = 20%, and determine the critical regions for the one-tailed test and for the two-tailed test of H0.

日本語版 は授業で話した内容で省略されたものなので英語版の方が正確 と考える。

Due: May 16, 2016 at 14:00.