# Unit 10: Hypothesis Tests

Read chapter 26 of FPP and do the following review exercises:
Chapter 26 (pages 497-501): 2, 3, 4, 5, 7

"Who'll Stop the Rain?," by Sharon Begley, Newsweek, "On Science" 15 column, August 4, 2008, page 56.
Available via LexisNexis Academic by searching for "Begley stop the rain".

## Possible Essay Questions:

• What is a "hydrometeor"?
• An article in the Irish Times shortly after the Olympics began reported that there was no rain on Beijing during the Friday opening ceremonies, but there was rain on Sunday. Does that mean Begley is wrong?

## Note:

The Final Project Progress Report is due with this unit assignment. See the final project guidelines for details.

## Computer project:

Suppose we want to test whether a particular coin is fair by tossing it 100 times and then using a test of significance. (The null hypothesis will be that the coin is fair.)

Preliminary writeup. Find the number of heads that corresponds to the cutoff for rejecting the null hypothesis of a fair coin using a two- tailed test for a significance level of 0.10, 0.05 and 0.01. [For example, to get a significance level of 0.10 in a two-tailed test, the desired z-value corresponds to an area of 100 - 2(5) = 90 percent, which the normal table says is z = 1.65. Since the null hypothesis implies an EV of 50 and an SE of 5, we should reject a result outside of the interval 50 plus or minus 1.65(5), i.e., from 41.8 to 58.3; these are the values that should go in the "bin array".]

What percentage of the tests should fail to get the correct result if the coin is actually fair when the significance level is 0.10, 0.05 and 0.1? Now a much more difficult question: Can we tell what percentage of the tests should fail to get the correct result when the coin is actually unfair? Explain.

Simulations: For each problem below, use a spreadsheet to implement 50 simulations of 1) tossing a coin 100 times and 2) applying a test of significance. For each problem, report the percentage of simulations where the test of significance failed to reach the correct decision. The letter p denotes the probability of a head on any given toss of the coin.

1. Use a fair coin (p=0.5) and a significance level of 0.1.
2. Use a fair coin (p=0.5) and a significance level of 0.05.
3. Use a fair coin (p=0.5) and a significance level of 0.01.
`=IF(RAND()<.55,1,0)]`