Notes for Homework 13, due Monday, Nov. 18 (not accepted late)

Notes on correlation

Notes for Homeowrk 12, due Wednesday, Nov. 13 (Monday is a holiday)

Notes on using the chi square table for the hypothesis test for the independence of a contingency table

Notes on the 95% confidence interval for values from opinion polls, often discussed as "the margin of error"
 

Notes for Homework 11, due Nov. 4

Using the chi-square table to get confidence intervals for the standard deviation of a population and goodness of fit, used to check to see if a probability distribution conforms to our idea of fairness.

 

Notes for Homework 10, due Oct. 28

Notes for comparing two proportions

Notes for comparing two averages

Notes for the matched pairs method of comparing averages

Notes for Homework 9, due Monday, Oct. 21

Notes for two tailed hypothesis testing on determining a fair coin or not

Notes for testing with t-scores and getting approximate p-values
 

Notes for Homework 7, due Mon. Oct. 7

Notes on confidence intervals for averages using t-scores

Notes for confidence intervals for opinion polls

Notes for the Confidence of Victory method
 

Notes for Homework 6, due Mon. Sept 30

Notes for Bayesian conditional probability

Notes for the expected value of a game

Notes for converting between classic and modern pari-mutuel statements of profit and risk.

Notes for Homework 5, due September 23

 Notes for the birthday problem

Notes for the Monty Hall problem

Notes for the probabilities of drawing cards from a deck

Notes for the odds of missing a rare side effect
 

 

Notes for Homework 4, due September 16

Notes on contingency tables

In Excel: the sum of a row will be of the form
=sum(a1:c1) where the letters are the changing indices

The sum of a column will be
=sum(a1:a5) where the numbers are the changing indices

Notes on the Central Limit Theorem

In Excel: In my version of Excel, the function that gives you the proportion less than a z-score is

=norm.dist(x, mean, standard_dev, cumulative)

The cumulative value should be 1 always.

If we are doing a Central Limit z-score based on the average of a sample, the instruction is changed as follows. 

=norm.dist(x, mean, standard_dev/sqrt(n), cumulative)

where n is the size of the sample.

Notes on probabilities of independent trials

In Excel: Again, different versions of Excel have different spelling of functions, and in my version the function is

=binom.dist(r, n, p, cumulative)

If cumulative = 0, you get the value of exactly r successes in n trials.

If cumulative = 1, you get the value of at least r successes in n trials.

Notes for Homework 2, due Wed., Sept. 4 (Monday is a holiday)

Notes for standard deviation and z-scores

Notes for z-scores to proportions and vice versa

Notes for Homework 1, due Mon. August 26, 2019

Notes on five number summary

Notes om mean, median and mode

Notes on frequency tables
 

Notes for Homework 12 and the link to the five British logicians

Notes on fractions to repeating decimals and vice versa

Notes on Roman numerals to Hindu-Arabic numerals and vice versa

Link to the biographies of Dodgson, Boole, Babbage, Lovelace and De Morgan

Notes for Homework 11

Notes for the chi square table: Confidence interval of a standard deviation and goodness of fit of a set of categories

Notes for Homework 10

Notes on hypothesis testing for two proportions

Notes on hypothesis testing for two averages - matched pairs and for separate, unrelated samples of the same measurement
 

Notes for Homework 9

Notes for the correction factor to approximate binomial distribution using normal distribution, z-scores and the green look-up table

Notes on t-scores, the yellow look-up table and hypothesis testing

Notes for Homework 7

Notes on t-scores

Notes on how to use the Population Pyramid website

Here are the cohort number for each gender and the total of the sexes from all the cohorts from 99 down. (The 100+ does not register at 0.1% for either males or females.) The cohorts in bold are the ones where the percentage is greater than the next youngest five year cohort.  If the birth rate about the same, you would expect that death rates would mean there would be less people in the 50-54 cohort than in the 45-49 group. In the United States, there was the big baby boom from 1945 through 1965. The last gasp of that increased birth rate is the reason the 50-54 cohort counts as a mode. We also had a smaller baby boom that ended in the past five years, the reason why the ages from 5-9 and 20-24 all count as modes. 

Cohort Male Female Total
95-99  0.0%  0.1%  0.1%
90-94  0.2%  0.4%  0.6%
85-89  0.5%  0.7%  1.2%
80-84  0.8%  1.1%  1.9%
75-79  1.2%  1.4%  2.6%
70-74  1.7%  2.0%  3.7%
65-69  2.4%  2.7%  5.1%
60-64  2.9%  3.1%  6.0%
55-59  3.4%  3.5%  6.9%
50-54  3.5%  3.5%  7.0%
45-49  3.2%  3.1%  6.3%
40-44  3.2%  3.2%  6.4%
35-39  3.1%  3.1%  6.2%
30-34  3.4%  3.5%  6.9%
25-29  3.5%  3.4%  6.9%
20-24  3.7%  3.5%  7.2%
15-19  3.3%  3.1%  6.4%
10-14  3.3%  3.1%  6.4%
05-09  3.3%  3.1%  6.4%
00-04  3.1%  3.0%  6.1%

Notes for Homework 6, Fall 2018

Link to the population pyramid website

Link to the New England Journal of Medicine page (click on the interactive graphic icon, needs Adobe Flash player)

Notes for Homework 5, Fall 2018

Notes on Bayesian method of probability

Practice for Bayesian and changing classic parimutuel to modern and vice versa

Expected value of a game
 

Notes for Homework 4, Fall 2018

Notes on the birthday problem

Notes on the Game Show Problem (a.k.a. the Monty Hall problem) all the way at the bottom of the post

Notes on missing a side effect in a study

Note on dependent probabilities for drawing cards from a deck without replacement