The lady tasting iced tea

As part of the parents involvement in my youngest son school, last Friday was the “parents teaching” day, where parents presented various topics that may interest the students. I chose to try the reproduce Fisher’s lady tasting tea experiment, but with a twist.

I started the class with general discussion on designing experiments, and presented the story of the lady and the tea. Then I asked them how they would test if the lady can actually tell whether the tea or the milk was added first to a cup. After a short discussion, the 11 years old students reached the design that Fisher used. Of course, I did not expect them to get into the statistical inference details.

Once we got a design, I pooled two bottles of iced tea out of my bag. In Israel there are two leading brands of iced tea, lets call them A and B. A few more minutes were needed to get to the design of an experiment for testing whether the kids can distinguish between the tastes of the two brands.

We used the following design:

  1. A flip of a coin determined if we will pour the same brand of iced tea into two cups, or pour one brand in one cup and the other brand into the other cup.
  2. In case the same brand should be poured into the two cups, another coin flip determined if it should be brand A or brand B.

Then, one of the students who was, of course, blinded to the process of filling the cups, tasted the tea in both cups and announced if she can distinguish between the tastes of the tea in each cup, and her answer was recorded.

The final results are [*]:

Was the taster right?
Yes No Total
Cups combination AB 5 5 10
AA or BB 4 3 7
Total 9 8 17

I think we can conclude that there is no evidence for rejecting the hypothesis that the students can distinguish between the tastes of the two brands (you are welcome to do your own statistical analysis).

On a personal note: from my point of view it was a great success, since my son, who refused tasting brand B was convinced to taste it, and admitted that he likes its taste.

[*] I know I should have recorded the outcomes of the re-randomization, so that the table will have 3 rows and not only two. You will have to forgive me. My only excuse is that was a fun demonstration for fifth graders.

Will baseball’s winning streak record be broken?

I came across this story in ESPN: Which of baseball’s most unbreakable records might actually get broken in 2019?
You can pass the story, unless you are really baseball statistics nerds, or don’t have something better to do, like me. But there is an interesting probability question there.
The longest winning streak in MLB history was 26 wins in a row, and this record was set by the Giants in 1916. What is the probability that this record will be broken?
The author, Sam Miller, argues that the chance is about 1 in 250. His reasoning goes along these lines: First he assumes that the best team will win about 100-110 games out of the season’s 162 games. The next assumption is that the probability of winning is the same for each game, therefore this probability ranges in 0.62 to 0.68. He does not state the third assumption explicitly, but you can’t do the math without it: games are independent.
All these assumptions translate to a series of 162 Bernoulli trial, with success probability of about 0.65 (plus/minus 0.03). So, what is the probability of getting a streak of at least 27 successes? Can you do the calculations?

This post was originally posted at Statistically Speaking.

Pi day quiz

Today is the Pi day – an annual celebration of the mathematical constant Pi. It is observed every year on March 14, since Pi can be approximated by 3.14, and the this date is written as 3/14 in the month/day format.

To celebrate this day, here is a short quiz about Pi. You can find all the answers on the web, but it is more fun to try answering while depending only on personal knowledge. Let’s go!

1) In the ancient world, many cultures derived approximations to Pi. Which ancient culture had the best approximation?
a. Egypt
b. Babylon
c. Hebrews
d. India

2) Which of these fractions is the best approximation Pi?
a. 2549491779/811528438
b. 22/7
c. 3927/1250
d. 864/275

3) Who popularized the use of the Greek letter Pi to represent the ratio of a circle’s circumference to its diameter?
a. Carl Friedrich Gauss
b. Leonard Euler
c. Pierre Simon Laplace
d. Issac Newton

4) The problem of squaring the circle does not have a solution because Pi is
a. An algebraic number
b. A rational number
c. A transcendental number
d. An irrational number

5) Who prove that the problem of squaring the circle does not have a solution?
a. Carl Friedrich Gauss
b. Adrien Marie Legendre
c. Ferdinand von Lindman
d. Evariste Galois

6) Pi plays an important role in Statistics because
a. The value of Pi can be approximated by dropping needles on the floor
b. The sample size calculation formula contains Pi
c. The probability density function of the Normal distribution contains Pi
d. Pi is the maximal value of Euler’s population density curve

7) Who was born on Pi day?
a. Johann Strauss
b. Wolfgang Amadeus Mozart
c. Johann Sebastian Bach
d. Georges Bizet

8) How many decimal digits of Pi were calculated up to date?
a. ~ 206 billion
b. ~ 50 quintillion
c. ~ 22.5 trillion
d. ~ 352 million

9) The first known rigorous algorithm for calculating the value of Pi was devised by
a. Shankara Variyar
b. Liu Hui
c. Archimedes
d. Ibn al-Haytham

10) Which of the following series does not converge to Pi?

Good luck! I will post the answers next week.