1
   

Family Wine Tasting

 
 
mrmac
 
Reply Wed 12 Dec, 2012 05:15 pm
I've tried this in two other places with no interest being shown. Perhaps it's too easy (but not for me), so I would appreciate any help.
______

Recently a group of 14 participated in a wine tasting. Wines were divided into 4 different categories (Zinfandel, Shiraz, Malbec, Cabernet Sauvignon) with 3 wines in each group. In a blind tasting, we were to determine whether a wine cost less than $10, $20 or more, or in between - one wine of each varietal in each price range. We weren't allowed to put, say, two Malbecs in the less than $10 category.

SAMPLE SPACE DELETED DUE TO FORMATTING

As a group, we picked a wine’s price point (cheap, mid, expensive) in slightly more than half of all tastings (53.5% of all answers correct). What would we have expected from a fictional group that made all of its selections randomly?

With respect to the 3 different categories (cheap, mid, expensive), we correctly identified the mid-priced wine only 45% of the time. We did better with the cheap and expensive categories. Is there anything of significance that can be deduced from that?

There is no money riding on this - only family honor.


Dick
 
View best answer, chosen by mrmac
dalehileman
 
  -1  
Reply Wed 12 Dec, 2012 05:52 pm
@mrmac,
Don't know about wine, but

http://www.realbeer.com/discussions/showthread.php?t=23994

http://www.realbeer.com/discussions/showthread.php?p=264242#post264242

OT but anyone wishing to discuss The Brew, I am [email protected],, recording Secretary of The Greater Southwest Beer-Tasting Society


We do however respect wine tasters
0 Replies
 
markr
  Selected Answer
 
  4  
Reply Wed 12 Dec, 2012 08:12 pm
@mrmac,
Assuming the varietals are known when tasted (i.e. you couldn't guess that the cheap Zin was an expensive Cab), a random assignment for a group of 3 would break down like this:
3 for 3: 1/6 of the time
1 for 3: 1/2 of the time
0 for 3: 1/3 of the time
Note: Can't go 2 for 3.

(3 * 1/6) + (1 * 1/2) + (0 * 1/3) = 1

Which means the expected number of correct guesses would be 1 (out of 3). You did better than random.

Regarding the poorer performance with the mid-priced wine:
You either get them all right, all wrong, or swap two of them
I think your results make sense since the least common errors would likely be mistaking a cheap for an expensive and vice versa. Therefore, you're probably most likely to mistake an expensive for a mid (and vice versa) or a cheap for a mid (and vice versa). In both cases, the mid-priced wine was involved, but each of the others was only involved in some fraction (summing to one) of those errors.
solipsister
 
  2  
Reply Wed 12 Dec, 2012 10:50 pm
@mrmac,
http://en.wikipedia.org/wiki/Binomial_distribution

Talk about using a sledge hammer to crack a nut.

3 random equal choices denotes a probability of 1/3 or the long way round:

Quote:
Assuming the varietals are known when tasted (i.e. you couldn't guess that the cheap Zin was an expensive Cab), a random assignment for a group of 3 would break down like this:
3 for 3: 1/6 of the time
1 for 3: 1/2 of the time
0 for 3: 1/3 of the time
Note: Can't go 2 for 3.

(3 * 1/6) + (1 * 1/2) + (0 * 1/3) = 1

Which means the expected number of correct guesses would be 1 (out of 3). You did better than random.


Given you were blind the normal approximation to the binomial is fraught to say nothing of the gallons of poisson distribution. Suffice to say the central limit theorum and a null hypothesis suggests you are a family of tipplers but significant evidence of taste buds is scant with 95% confidence.



markr
 
  1  
Reply Thu 13 Dec, 2012 02:20 am
@solipsister,
Beats using a screw driver. What problem are you solving such that your link to the binomial distribution is relevant?
mrmac
 
  1  
Reply Thu 13 Dec, 2012 08:06 am
@markr,
markr - thank you very much for your prompt reply. My argument was virtually identical to yours. I made the case that poor performance with the mid-priced wine was a positive, all other things being equal - better to switch two adjacent price range wines than to mistake the cheap for the expensive and vice versa.

My family members have not been convinced by my logic, so if you would just confirm that you are Chairman of the Mathematics Department at MIT, I'll be all set.

The only thing that I haven't tried is to get them to set up an experiment with playing cards and get their results empirically. That's how I was able to convince my 7th grade students "to switch" when confronted with the Monte Hall problem.



markr
 
  4  
Reply Thu 13 Dec, 2012 10:29 am
@mrmac,
Cal Tech, but close enough...
mrmac
 
  1  
Reply Thu 13 Dec, 2012 03:24 pm
@markr,
graduate, graduate student, ???
markr
 
  1  
Reply Thu 13 Dec, 2012 05:56 pm
@mrmac,
I'm joking (since I thought you were, too). I do have a degree in math from UCSD several decades ago.
ossobuco
 
  1  
Reply Thu 13 Dec, 2012 06:08 pm
@markr,
I'm just a reader, dumb re math. I lived in La Jolla in '64: good grand rounds at the then Scripps Institute, where I was a peon.

Keep on with the talk, eh?
markr
 
  2  
Reply Thu 13 Dec, 2012 06:45 pm
@ossobuco,
We moved to SD from the east coast in '69 when I was a kid. I graduated in '82, and left the city in '91 - too crowded, which is a shame because the weather is superb. I'm now in San Luis Obispo county.
ossobuco
 
  1  
Reply Thu 13 Dec, 2012 07:04 pm
@markr,
But I like that area.. alway have.

I can't talk math to you, but perhaps wine. I've been to a lot of the area vinyards but I don't talk wine too well either. Hey - I think the countryside there is beautiful, shoulder settling. I'm basically from Venice, and my husband and I sometimes used to set off for a few days drive, usually ending in your area or the paso robles area.

I've some friends with a property up near 46 - they were hit with a big
earthquake when first there.

Anyway, nice to talk. I'll be quiet for a while as I'm talking in a math thread.
markr
 
  1  
Reply Thu 13 Dec, 2012 07:24 pm
@ossobuco,
I'm just south of Paso Robles.
0 Replies
 
ossobuco
 
  1  
Reply Thu 13 Dec, 2012 07:42 pm
@ossobuco,
Ah - I don't suppose Templeton? I liked Templeton when I was there. Not my business of course, where you are, but I liked the town. We stopped at a somnulent cafe for a burger (or what) and they had good short wine by the glass list. That's not usual, even in the spiffy parts of Los Angeles.
solipsister
 
  1  
Reply Thu 13 Dec, 2012 09:15 pm
@markr,
Now, now dear, just because I opprobriated your prolix proof is no reason to go all probe and ballistic on me.

The question was:

Quote:
What would we have expected from a fictional group that made all of its selections randomly?


I was alluding to comparing the actual results with a random expectation of 1/3 by way of a normal approximation to the binomial, in the absinthe of the complete results, but shirley you knew that.

markr
 
  1  
Reply Fri 14 Dec, 2012 12:10 am
@ossobuco,
Bingo!

Well, this is wine country...
0 Replies
 
markr
 
  1  
Reply Fri 14 Dec, 2012 12:19 am
@solipsister,
Pointing someone to the binomial distribution article doesn't explain the solution. It doesn't apply to this problem. If you're going to diss my explanation, at least provide an appropriate (and preferably better) one.
solipsister
 
  1  
Reply Fri 14 Dec, 2012 12:37 am
@markr,
Quote:
If you're going to diss my explanation, at least provide an appropriate (and preferably better) one.


I already did. 3 choices randomly means a probability of 1 in 3.

Quote:
Pointing someone to the binomial distribution article doesn't explain the solution.


I wasn't seeking to explain your long-winded method of arriving at 1/3, I was referring to analysis of the statistics.
markr
 
  1  
Reply Fri 14 Dec, 2012 12:46 am
@solipsister,
Well then maybe you can explain how it applies to this problem.
mrmac
 
  2  
Reply Fri 14 Dec, 2012 04:56 am
@markr,
I was joking - but then hoped that you weren't! I do appreciate your help and your clear explanation.
0 Replies
 
 

Related Topics

Probability of 11 cards - Question by ptkaisen
Probability - Question by sean2
Exercise in Probability!!! - Question by evinda
Winning chance - Question by ghodhereek
what is the probability of... #4 - Question by w0lfshad3
The chances of a higher power. - Question by ascribbler
 
  1. Forums
  2. » Family Wine Tasting
Copyright © 2019 MadLab, LLC :: Terms of Service :: Privacy Policy :: Page generated in 0.05 seconds on 05/26/2019 at 08:57:23