STAT460 - Experimental Design
Daily Homework #2 - Box/Hunter/Hunter II

Part 1:

In class today, we reviewed the mechanics of three basic calculations (originally covered in your introductory statistics course). Review these mechanics by doing the following computations using the indicated method.

a) Find the sample standard deviation of the numbers 8, 9, 4, 3, 1. (Do this by hand.)

b) Find the sample standard deviation of the numbers 32.47, 39.53, 37.42, 31.63. (Do this using either your calculator or a spreadsheet.)

c) IQ's are normally distributed with a mean of 100 and a standard deviation of 16. Find the probability that a randomly selected person has an IQ of 120 or higher. (Do this both by hand using a table, and using a spreadsheet's intrinsic function.)

d) Find the probability that an observation from a Student's t distribution, with 12 degrees of freedom, is equal to 2.34 or higher. (Again, do this both by hand using a table, and using a spreadsheet's intrinsic function.)

Part 2:

We continue with our reading of Statistics for Experimenters by Box, Hunter and Hunter ("BHH").

1) Skim Section 2.4, which covers some concepts and technical computations which we went over in class in more detail. Based upon your reading, and the class lecture, briefly explain the following concepts (in your own words):

a) degrees of freedom

b) normal distribution

c) central limit theorem

d) Student's t distribution

2) Now read in detail Section 2.5. Reproduce the calculations described in the section. (Use a spreadsheet.) Answer the following questions.

a) Why are BHH doing these computations? (Be specific: not just "well, they're testing this hypothesis thingie" but the motivations behind the particular computations that are being done.)

b) Why does their variance estimate have 10 (= n) rather than 9 (= n-1) degrees of freedom?

3) Do Exercise 2.14, parts A and B (p. 53).

SOLUTIONS to Part 1:
a) 3.39     b) 3.82      c) 0.10565     d) 0.0187