My re-sit for statistics Watch

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Sleepwalker
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Hi,
Can anyone help me with a problem I have urgently? I am a student at University, studying Business Information systems, unfortunetly I have to resit my exam in Maths (statistics) which I'm hopeless at. I can understand and work out most of the questions but stuck on a few. I know what u'z are all thinking, (why don't I just get help, from the Lecturer that took me in the first place) I would if I could, but apparently the Lecturer is away untill 2 days before the resit, (which isn't much of a help). So I was depending on anyone that would be so kind on here to help me. If there is anyone out there that can help please email me and I will send you a copy of the papers that I have been revising from and the ones that I am stuck on. It would be much appericated.
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ickle_katy
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(Original post by Sleepwalker)
Hi,
Can anyone help me with a problem I have urgently? I am a student at University, studying Business Information systems, unfortunetly I have to resit my exam in Maths (statistics) which I'm hopeless at. I can understand and work out most of the questions but stuck on a few. I know what u'z are all thinking, (why don't I just get help, from the Lecturer that took me in the first place) I would if I could, but apparently the Lecturer is away untill 2 days before the resit, (which isn't much of a help). So I was depending on anyone that would be so kind on here to help me. If there is anyone out there that can help please email me and I will send you a copy of the papers that I have been revising from and the ones that I am stuck on. It would be much appericated.

i did a-level statistics....so if any of that covers the same areas??? d's the only person i know thats in uni..so he may know?

why dont you post a question and together we'll try and solve it?!?

love Katy ***
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Sleepwalker
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(Original post by ickle_katy)
i did a-level statistics....so if any of that covers the same areas??? d's the only person i know thats in uni..so he may know?

why dont you post a question and together we'll try and solve it?!?

love Katy ***
Hi Katy
Thanx for replying so quick, ok here go's this is one of the questions I am stuck on.



For Four theatres in a city, the following are the numbers of male and female callers phoning to buy tickets during a typical week.

Sex of caller A B C D TOTAL
Male 28 47 21 38 134
Female 32 48 54 12 146
Total 60 95 75 50 280



a) What would be an appropriate statistical test for these data to test for independence of Theatre choice and gender?

b) State the null hypothesis and conduct the test identified in part (a)
Test at the 5% significance level.


c) what conclusions can you draw from your analysis?
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Unregistered
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Do u go to middlesex university by any chance?
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Sleepwalker
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(Original post by Unregistered)
Do u go to middlesex university by any chance?

Nope I'm in Liverpool, y are you having the same problem?
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ickle_katy
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the answer to b part one is "that the choice of theather is independant of the gender of the caller" or something like that.


i'll get back to you with the rest in the morning when my brain works better. or at least ill read it more carefully!

love Katy ***
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Sleepwalker
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(Original post by ickle_katy)
the answer to b part one is "that the choice of theather is independant of the gender of the caller" or something like that.


i'll get back to you with the rest in the morning when my brain works better. or at least ill read it more carefully!

love Katy ***
Katy
Would you be kind enough to explain step by step on how you come to that conclusion (tomorro if that's ok with you), as I want to learn myself.


Thanx
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Sleepwalker
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(Original post by Sleepwalker)
Katy
Would you be kind enough to explain step by step on how you come to that conclusion (tomorro if that's ok with you), as I want to learn myself.


Thanx
Is there anyone that can help me with this problem??? I'm not trying to get a quick answer I really want someone to talk it through with me step by step so i understand it proparely.


I'd be most grateful
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Jonny W
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The model for the experiment is that we choose n = 280 callers to the four theatres at random. These 280 observations are independent and each can have one of eight outcomes:

(Male, A), (Male, B), (Male, C), (Male, D),
(Female, A), (Female, B), (Female, C), (Female, D).

Let p(i, j) be the probability of sex i and theatre j.

Let x(i, j) be the number of observations of sex i and theatre j.

We want to test the null hypothesis that the sex of a caller is independent of the theatre they are calling. So the null hypothesis is that

p(i, j) = p(i) * q(j) for some probability distributions p(i) and q(j).

The alternative hypothesis is that p(i, j) is unrestricted.

Now we define the statistic

X = (sum over i, j) (x(i, j) - e(i, j))^2 / e(i, j)

where e(i, j) is "what we would expect x(i, j) to be if the null were true", so

e(i, j) = (sum over k) x(i, k) * (sum over k) x(k, j) / (sum over k, l) x(k, l).

Under the null, the distribution of X is approximately chi-squared(3). (See below for where the "3" comes from.) If the null is false, X tends to be larger. So the test is: reject the null if X >= K, where K is chosen so that

P(chi-squared(3) >= K) = 0.05.

Where does the "3" come from?

Short answer. For this type of problem it's always

(number of rows - 1)*(number of columns - 1)
= (2 - 1)*(4 - 1) = 1 * 3 = 3.

Long answer. Under the alternative, p(i, j) has seven "free parameters": once we have specified p(i, j) for seven choices of (i, j), the eighth is determined by the constraint that

(sum over i, j) p(i, j) = 1.

Under the null, p(i, j) has four "free parameters": one for p(i) and three for q(i). To get the "3" we calculate:

"number of free parameters under alternative"
- "number of free parameters under null"
= 7 - 4 = 3.
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Jonny W
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As a followup to my last post, here's a step-by-step guide to doing the test.
  1. Calculate (sum over k) x(i, k) for all i. (That is, add up each row.)
  2. Calculate (sum over k) x(k, j) for all j. (That is, add up each column.)
  3. Calculate (sum over k, l) x(k, l). (That is, add up everything.)
  4. Calculate e(i, j) for all i and j.
  5. Calculate X.
  6. Find K in some statistical tables, or work it out on a computer.
  7. Is X >= K? If so, reject the null hypothesis. Otherwise accept it.


Please let me know how you get on.

Jonny.
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