Testing of Hypothesis

#1
A company developed synthetic coffee and claim that coffee drinkers could not distinguish it from the real product. A number of coffee drinkers challenged the company's claim, saying that the synthetic coffee tasted synthetic. In a test, carried out by an independent consumer protection body, 20 people were given a mug of coffee. Ten had synthetic brand and ten the natural, but they were not told which they had been given. Out of the ten given the synthetic brand, eight said it was synthetic and two said it was natural Use this information to test the coffee drinkers' claim as against the null hypothesis of the company's claim, at 5% significance level.
 

alberto

New Member
#2
1) For students of statistics: Please try the problem on your own first, and tell us what you have done so far. The more information we have, the better we can help you. Please don't expect quick solutions to your homework. We'll help you get started, exchange ideas, how-to's, etc. but only if you show that you are willing to learn and put in effort as well.
anyway....the test you are asked to do looks like the "sign test", which is a "binomial test".

further hint: this is the observed distribution of the ten drinkers with the fake coffee..... (I'm one of the eight....I'm italian!). for you help I marked also all the significant level on each istogram bar....it will be very easy for you now to understand in which region you are: Acceptance or Rejection


Immagine.jpg
 
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alberto

New Member
#4
Hi @Karabiner: can you please explain which is the error in my brainstorming? Isn't it the same prolem as the following?

tossing a coin 10 times you get 8 heads. Is it a fair coin or not?
If the number of tossing was grater you can use other tests, i.e. chi-squared, but with only 10 tosses I think that a non parametric approach with the binomial test is correct.

Going back to the original question, as you can see, I already warned the OP first.

best regards
 
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Karabiner

TS Contributor
#5
I referred to your recommendation of the sign test, which is a test for an ordinal
scaled outcome, not a binary outcome; and it is a test for 2 dependent samples,
but here we have 2 independent samples. But maybe I misunderstood your statement.

Likewise, the binomial test is not the solution here, in my opinion, as long as we assume
that the "natural brand" condition was not introduced just to lead the problem solvers
astray.

With kind regards

Karabiner
 

alberto

New Member
#6
the way to approach the problem are more than one (for example I'd like to attack it in a Bayesian way).
But I think that the most natural and intuitive way is to state the Hypothesis System as follows:

H0: the Company claims that the decision of a drinker to say: natural of fake (I remember a classic example where an old English lady was sure to detect if in the cup of tea you poured milk ore tea first....and she guessed every time!) is like tossing a fair coin: Head for natural and Tail for fake.

in formula:

Immagine.jpg

so, considering the diagram of the observed 10 size sample it is obvious that you reject the Statement of the Company if and only if the observed sample has a number of success >8 or <2, with a p-value <=5%

It is understood that this is only my opinion, and I am not a teacher but only an old guy.


Just a question: I am just registered here and I was not able to find a way to write the formulas in LaTeX or similar format. Can you help me?

thanks in advance
 
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Karabiner

TS Contributor
#7
After re-reading the initial post I can see now what I had overlooked.

I am not quite convinced by an expected proportion of 50%, i.e. that
mere guessing is the correct model here. We need to include the
"natural" condition if we want to answer the question whether synthetic
coffee is more often experienced as tasting synthetic than natural coffee.

But the problem description did not include the responses from the
control group (natural coffee), and seemingly the "natural brand"
condition was indeed introduced just to lead the problem solvers
astray. Therefore you seem to be correct to consider this as a one-sample
problem.

With kind regards

Karabiner
 

alberto

New Member
#8
We need to include the
"natural" condition if we want to answer the question whether synthetic
coffee is more often experienced as tasting synthetic than natural coffee.
..of course.

But the problem description did not include the responses from the
control group (natural coffee), and seemingly the "natural brand"
condition was indeed introduced just to lead the problem solvers
astray.
...this is exactly what I mean (unless the OP didn't forget to include the responses from the control group....)

I hope that the OP will understand how important is to write down the entire and original text....and show his effort to solve the problem