Apples and Pears

#1
Hi all,

I have a challenge for you, this might be quite easy or quite difficult... as I neither know the answer nor have any idea of the solution. Sorry if it's too tough (or too easy)!


A grocer wants to compare the relative weight of apples and pears.

He starts weighing the fruit, and weighs 19 apples and 14 pears before he gets bored and checks his results.

Apple Weights (grams):
145,148,128,266,115,154,260,239,240,150,236,239,280,185,263,173,111,296,248

Pear Weights (grams):
140,142,148,121,130,124,141,130,149,121,124,128,121,143

So on average, apples weigh 204g and pears weigh 133g.

He concludes that on average apples weigh 34.8% more than pears.

The question is, how reliable is this result? (Could the reliability be expressed as a %? E.g could he be 95% sure that apples are (say) at least 33% bigger than pears?)

And how would the reliability vary if he included more or less apples and/or pears in the test?

Hope that made sense, thanks in advance for any ideas! :tup:
 

vinux

Dark Knight
#2
Hi all,


He concludes that on average apples weigh 34.8% more than pears.

The question is, how reliable is this result? (Could the reliability be expressed as a %? E.g could he be 95% sure that apples are (say) at least 33% bigger than pears?)

And how would the reliability vary if he included more or less apples and/or pears in the test?

Hope that made sense, thanks in advance for any ideas! :tup:

The problem is interesting. But the measure you use for comparison of apples and pears are not;).
How you came the figure % 34.8. It must be (1- 133/204)*100 .

Now the question part.
how reliable is this result?
How do you define the term reliable?:rolleyes:.

Usually how we tackle this is
we find out the distribution weight of Apple and Pears ( X-weight of Apple , Y weight of Pear)
and suppose there are n1 apples and n2 pears. and Xbar and Ybar are averages...

Then We find out the distribution of 1-Ybar/Xbar ( i hope you have used this formula for comparison)

It will be in terms of n1 and n2

Here you can find out the confidence interval of the mean and see how n1 and n2 will affect the CI
 
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#3
Thanks Vinux,

Of course you are right :yup: The apples weigh 53.4% more than the pears...
(it's the pears that weigh 34.8% less than the apples).

Your answer is very interesting... a bit over my head, I must admit!

How about calculating the variance of the difference between every possible combination of 1 apple and 1 pear?
I.e. 19 (apples) x 14 (pears) = 266 values...

Is that a useful calculation? I don't know how to use confidence intervals... I need to do some reading. :confused: