# Thread: Statistics Marathon & Questions

1. ## Re: University Statistics Discussion Marathon

I am thinking the 2nd and 4th apply

y>=32
1:50

Just from using R

2. ## Re: Statistics

Quick question regarding probability spaces:

$\text{Is the convention to take }\mathbb{P}(A) \ge 0\text{ or }\mathbb{P}(A) > 0?$

3. ## Re: Statistics

Originally Posted by leehuan
Quick question regarding probability spaces:

$\text{Is the convention to take }\mathbb{P}(A) \ge 0\text{ or }\mathbb{P}(A) > 0?$
Greater than or equal to. Events can have 0 probability.

4. ## Re: Statistics

leehuan - what would you do if InteGrand decides to take a 6 month sabbatical?

5. ## Re: Statistics

Originally Posted by Drongoski
leehuan - what would you do if InteGrand decides to take a 6 month sabbatical?
I don't know; InteGrand can do as he wants. But why are you asking me this?

6. ## Re: Statistics

Originally Posted by leehuan
I don't know; InteGrand can do as he wants. But why are you asking me this?
Just teasing you. And noting that InteGrand has been helping you so much.

7. ## Re: Statistics

Originally Posted by Drongoski
Just teasing you. And noting that InteGrand has been helping you so much.
Very true. So grateful.

8. ## Re: Statistics

I wasn't taught the hypergeometric distribution properly so can someone walk me through how to use it? Here's my question if it helps to refer to it.

A factory produces 80 items in a batch. To test if the batch is defective, an acceptance sampling scheme is adopted: a random sample of 10 items is selected, and if 2 or more items don’t meet customer specifications, the batch is considered defective.

If there are actually 11 defective items in the batch,

1i) What is the probability that 2 sampled items are defective?
ii) What is a general formula for x sampled items being defective?

9. ## Re: Statistics

Doing this for the first time for a very very long long time. Not sure if correct.

$P(X = k) = \frac{{\binom K k } {\binom {N-K} {n-k}}}{\binom N n} \\ \\Here N = 80, K = 11, n = 10 and for (i) k = 2 \\ \\ So: P(X = 2) = \frac {\binom {11} 2 \binom {80-11}{10-2} }{\binom {80} {10}} \\ \\ For k = x: P(X = x) = \frac {\binom {11} x \binom {80 - 11} {10-x}}{\binom {80} {10}}$

10. ## Re: Statistics

Originally Posted by Drongoski
Doing this for the first time for a very very long long time. Not sure if correct.

$P(X = k) = \frac{{\binom K k } {\binom {N-K} {n-k}}}{\binom N n} \\ \\Here N = 80, K = 11, n = 10 and for (i) k = 2 \\ \\ So: P(X = 2) = \frac {\binom {11} 2 \binom {80-11}{10-2} }{\binom {80} {10}} \\ \\ For k = x: P(X = x) = \frac {\binom {11} x \binom {80 - 11} {10-x}}{\binom {80} {10}}$
I think the expressions are right.

But I'm not sure what the parameters mean either. This question is pretty much an example but for an arbitrary scenario how would I be able to tell what the parameters (N, K, n) actually meant?

11. ## Re: Statistics

Originally Posted by leehuan
I think the expressions are right.

But I'm not sure what the parameters mean either. This question is pretty much an example but for an arbitrary scenario how would I be able to tell what the parameters (N, K, n) actually meant?
The parameters are as follows:

• N is the total population
• K is the number of "tagged" objects (defective objects in your example)
• n is the size of our sample.

The hypergeometric distribution pmf Drongoski wrote (in terms of the parameters N, K, n) then gives the probability that our sample has exactly k "tagged" (defective) objects present, under the assumption that we are sampling without replacement. This follows from basic combinatorics.

12. ## Re: Statistics

The reason for terms like "population" and "tagged" is that one place this distribution comes up is in ecology when we tag some members of an animal population (like a fish population) and then later draw (without replacement) a random sample from the animal population and count how many are tagged. This can be used to try and estimate the total population for example (it is sometimes known as the "capture-recapture method", and you can read more about it here: https://en.wikipedia.org/wiki/Mark_and_recapture).

13. ## Re: Statistics

Any tips for catching up on stats... like any resources you use?

Thanks I am behind lol.

14. ## Re: Statistics

Can't deny it. I'm also a fair bit behind.

Been cramming a lot of the course pack tbh.

15. ## Re: Statistics

Originally Posted by leehuan
Can't deny it. I'm also a fair bit behind.

Been cramming a lot of the course pack tbh.
what course pack? the questions that are on moodle or?

16. ## Re: Statistics

Originally Posted by Flop21
what course pack? the questions that are on moodle or?
Course pack is just what I use to call the online 'textbook' thing. It's like what we had in first year except it's just not printed.

17. ## Re: University Statistics Discussion Marathon

Q1. If we have a data set where the median is significantly greater than the mean, which of the following is likely to be true?

A. The data is left skewed
B. There has been an error in data input
C. Categorical data is being treated as numeric data
D. The data is right skewed

18. ## Re: University Statistics Discussion Marathon

Based on those diagrams, the answer should be A. Left skewed.

19. ## Re: University Statistics Discussion Marathon

A national TV poll is run asking viewers to ring in regarding whether they think the
head of the Australian Bureau of Statistics should be sacked over the problems with the
census. 500,000 people ring in, with 83% of respondents claiming he should be sacked.
Which one of the following is correct?
(1 mark)

A. The biggest problem with this survey is that people under 18 may have responded.

B. We conclude that majority of Australians believe he should be sacked.

C. The sample size is large enough to overcome any doubts about the validity of this
sample.

D. The results are unreliable as they quite likely suffer from self-selection bias.

20. ## Re: University Statistics Discussion Marathon

Id rule out D straight away in that question.

This from Wikipedia:

"In statistics, self-selection bias arises in any situation in which individuals select themselves into a group, causing a biased sample with nonprobability sampling. "

21. ## Re: University Statistics Discussion Marathon

Id rule out A straight up as well, which would love me down to B or C.

22. ## Re: University Statistics Discussion Marathon

Statistical validity refers to whether a statistical study is able to draw conclusions that are in agreement with statistical and scientific laws. This means if a conclusion is drawn from a given data set after experimentation, it is said to be scientifically valid if the conclusion drawn from the experiment is scientific and relies on mathematical and statistical laws.

id also refer out C, and would go for B in this question.

23. ## Re: Statistics

is there an easy way to find the probability mass function??

right now im just looking at example P(X=x) like P(X=1... etc.) and trying to find a pattern

but this is hard for tricky ones

24. ## Re: Statistics

Originally Posted by Flop21
is there an easy way to find the probability mass function??

right now im just looking at example P(X=x) like P(X=1... etc.) and trying to find a pattern

but this is hard for tricky ones
Got an example question?

25. ## Re: Statistics

Originally Posted by He-Mann
Got an example question?
A box contains four red and two black balls. Two balls are drawn. Let X be
the number of red balls obtained. Find fX(x)

Okay so if I haven't screwed up, P(X=0) = 1/15, P(X=1) = 4/5, P(X=2) = 2/5, and any other value of X, P = 0.

So how do I put this into a proper answer for this question?

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