Hi Vanessa
Let's try and get something a bit different going on here rather than
pelting allstat with questions out of a college book (okay so it's not
technically homework in the sense that noone has ordered you to do it,
but that distinction probably won't be appreciated by some on here).
Help us to help you a bit and tell us who you are and what exactly you
are trying to achieve.
You've posted some statistical type questions and a rather more
general maths type question. Let's take the latter first. There are
two ways of approaching this type of problem. One is what the
mathematicians call "brute force". This means, that, in common with
lots of problems, involving numbers, you can get to the answer simply
by sifting the possibilities rather than doing anything mathematical
or intuitive. This question is obviously of that type. In order to
move on from this question, you need to grasp hold of the (very
simple) operation that you need to perform with the two quantities
involved, namely the number of locations and the number of activities.
In other words, how would you answer the question if there were
123,456 states and 7,890 activities?
The statistical questions have a flavour of coming from a course that
is not mainly concerned with statistics. The questions are pitched at
a somewhat more elementary level than an undergrad course purely to do
with statistics. You need to start thinking statistically about it,
which I don't think at the moment from your comment that you are
doing. In just about any statistical situation, you have a
"population" mean that you never know but which you are trying to
estimate by collecting data. The estimates that you get are called
sample means and theory says that you expect to get the same value as
the "population" mean but you have to deal with biases and
uncertainties. This question is about the uncertainty surrounding an
estimate, and not the estimate itself, which we will take at face
vale. The uncertainty is called the "standard error " of the mean.
There is a general principle connecting sample sizes and standard
errors in any stats situation, as Helene hinted with her more specific
example.
There is a mathematical result concerning how the variance (and also
the standard deviation which is the square root of the variance) of a
variable Y is connected to the variance of a variable X when X and Y
are related. If you look up this result
e.g. google " variance of Y = aX" (where a is some number) . For
example, under the wikipedia entry on variance you will find the
answer you require under "basic properties".
regards
Andy
On 30 March 2015 at 14:03, Vanessa Narayanassamy <[log in to unmask]> wrote:
> Hello,
>
>
>
> This summer, a family knows they will take their vacation in Michigan,
> Minnesota, or Wisconsin.
>
> While on vacation, their main activity will be hiking or bicycling.
>
> How many combinations of main activity and state (for example, bicycling in
> Wisconsin) are possible?
>
>
>
> Just let you know this is not a homework. I am only practising permutations
> as I feel I have some weaknesses in this topic.
>
>
>
> Vanessa
>
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>
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>
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