Days 11 - 20

Sanderson M. Smith


Day #11:

"There are no facts, only interpretations."


Test day.

Day #12:

"To guess is cheap. To guess wrongly is expensive."


Produce graphical display of the empirical results obtained from simulation: A company has 20 employees, including 6 minorities. After a productive year the company decides to award each of 5 randomly selected employees a bonus of $5,000 each. The company does the selection process and it turns out there are no minorities among the selected five. There is suspicion that discrimination was involved in the selection process. That is, the randomness of the process is called into question. Statistically speaking, is there significant evidence to suggest the selection process was not random. (Use set of 20 dice... 14 white and 6 red.) Produce spreadsheet displaying the empirical distribution of the random variable x, where x is the number of minorities in the selected group of five employees.

Day #13:

"We don't know a millionth of one percent about anything.


Add the theoretical probabilities to the spreadsheet produced in the assignment for Day #12.


Day #14:

"There are no facts, only interpretations."


This day involved spreadsheet instruction. Of particular importance was the introduction of the COMBIN formula on Excel.

nCr is written COMBIN(n,r) in Excel.

For instance, the Excel formula =COMBIN(5,2) yields the number 10, which is equivalent to

5C2 = (5!)/[(3!)(2!)] = 10.

Day #15:

"Statisticians are not number librarians."


Class Activity: The STATISTICS class contains 9 girls and 5 boys, a total of 14 students. The instructor chooses four students. The chosen students turn out to be all boys. The question


was examined.

Day #16:

"All models are wrong. Some models are useful."


ASSIGNMENT: The STATISTICS class contains 9 girls and 5 boys, a total of 14 students. If a random sample of six students is chosen from the class, and if X represents the number of girls, then X is r random variable that can assume the values 0,1,2,3,4,5,6, Construct a spreadsheet that calculates the theoretical probability for each value of X, and produce a graphical display showing these probabilities.

Class activity involved a Quality Control simulation that set up the project for Day #17.

Day #17:

"There are no facts, only interpretations."


ASSIGNMENT: Begin construction of spreadsheet to address the QUALITY CONTROL situation described as follows: A company mass produces GIZZMOS. The manufacturing process is such that 20% of the GIZZMOS produced have minor defects that must be corrected by human contact before they are put on the market for sale. Periodically, a random sample of 25 GIZZMOS is chosen to inspect. Let x = the number of defective GIZZMOS in the sample. It is decided that x will be considered statistically significant if the probability of obtaining x defective GIZZMOS is less tan 5%. (Company will carefully examine production process if results are statistically significant.

QUESTION: What is the smallest value of x that will be considered statistically significant?

Constructed spreadsheet should include: (A) Premise; (B) Empirical and Theoretical Results; (C) A corectly-stated conclusion.

Day #18:

"What we have to learn, we learn by doing."


Activity involved an analysis of the following situation: During the course of one hour, each of two individuals arrives at a specific location, remains for exactly ten minutes, then departs. If the two arrival times are totally random, what is the probability that they meet? (Class did a simulation... and then used basic algebra and geometry to come to a theoretical probability.)

Day #19:

"Mathematics seems to endow one with something like a new sense."


Analysis of the game of SPADES (as created by former Cate student Whitney Abbott): This is a casino game. Player pays $1 for the right to be dealt five cards from a thoroughly shuffled deck. Player wins $1 for each spade in hand. Let x = the number of spades in a five card hand. Then x can assume values 0,1,2,3,4,5. Create a spreadsheet displaying the theoretical probabilities for each value of x.

Day #20:

"There are three kinds of lies: lies, damn lies, and statistics."


This day was used for more spreadsheet instruction. Emphasis on getting accurate and neat spreadsheets. A key theme was to get across the idea that one should determine what the spreadsheet should display before actually doing the construction. (Don't PUT THE CART BEFORE THE HORSE.)