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A statistic is a random variable that is a function from known observations of a population.....glorious 
It definately looks like an easy unit. However, its very easy to make a mistake if you don't read the questions properly. Just done a paper and got 51% but I suppose I should bear in mind I've done nothing on S2 since I finished it over a month ago. Hypothesis testing looks a bit confusing, forgotten exactly how its done. 
Basically this is what I can remember from S2 in a nutshell.
Two distributions - binomial and poission
Make sure you know the formula's for both these distributions and know how to use the tables. Also, don't get confused on the inequalities. You could be asked to use the poisson as an approximation to the binomial. I'm sure there's a consensus that this is the easiest part of S2 so probably best not to spend too much time on it.
Continuous random variables
Remember that a p.d.f. is the little f (f(x) and a c.d.f. is the big F (F(X)). If you want to get from a p.d.f. to a c.d.f. then you integrate and to get from a c.d.f to a p.d.f. you do the opposite (differentiate). You could be asked to draw a graph of these and work out the mode, E(X) (mean), Var(X) (variance), and the quartiles (F(Q1) = 1/4, etc).
Continuous distributions
I think here that you can be asked about the rectangular distribution. Don't really remember much about this as we went through it quite quickly.
There's also the normal as an approximation to the poisson and the binomial in this chapter. Remember to use the continuity correction.
Hypothesis testing
This is probably where they'll give you the worded questions so make sure you can remember all the definitions. This is likely to be at the end of a binomial or a poisson question from what I've seen.
Two distributions - binomial and poission
Make sure you know the formula's for both these distributions and know how to use the tables. Also, don't get confused on the inequalities. You could be asked to use the poisson as an approximation to the binomial. I'm sure there's a consensus that this is the easiest part of S2 so probably best not to spend too much time on it.
Continuous random variables
Remember that a p.d.f. is the little f (f(x) and a c.d.f. is the big F (F(X)). If you want to get from a p.d.f. to a c.d.f. then you integrate and to get from a c.d.f to a p.d.f. you do the opposite (differentiate). You could be asked to draw a graph of these and work out the mode, E(X) (mean), Var(X) (variance), and the quartiles (F(Q1) = 1/4, etc).
Continuous distributions
I think here that you can be asked about the rectangular distribution. Don't really remember much about this as we went through it quite quickly.
There's also the normal as an approximation to the poisson and the binomial in this chapter. Remember to use the continuity correction.
Hypothesis testing
This is probably where they'll give you the worded questions so make sure you can remember all the definitions. This is likely to be at the end of a binomial or a poisson question from what I've seen.
Im doing this paper too, gl everyone 
I wont be revising until Thursday/Friday either though, because of my physics... but when I get to it, I'll post on this more.
btw, all wordy questions are pretty much listed with their definitions at the back of the hypothesis testing chapter, including all of the Jan 05 wordy questions... I would highly advise to do what Im doing and learn them off by heart... there arent that many and for each of the definitions they give, you'd get all the points they want and all the marks for it, so well worth doing if you can!
I wont be revising until Thursday/Friday either though, because of my physics... but when I get to it, I'll post on this more.
btw, all wordy questions are pretty much listed with their definitions at the back of the hypothesis testing chapter, including all of the Jan 05 wordy questions... I would highly advise to do what Im doing and learn them off by heart... there arent that many and for each of the definitions they give, you'd get all the points they want and all the marks for it, so well worth doing if you can!
Chris87
Continuous distributions
I think here that you can be asked about the rectangular distribution. Don't really remember much about this as we went through it quite quickly.
I think here that you can be asked about the rectangular distribution. Don't really remember much about this as we went through it quite quickly.
Rectangular distribution is pretty easy and simple... its (dundundun) a rectangle... on a graph that is, because at any point the probability is the same.
ie a clock, the probability (considering only hours) that the hour is any time is equally distributed between 0 and 12 (0 and 12 being the ends of the rectangle) so, obviously the expected value is just half this, is (A+B)/2 or 6 in this case. Both Varience and Exp(X) are given in the formula booklet anyways, so really its a sinch.
Can someone help me with these questions on hypothesis testing please? Thanks.
Only need help with the last part of question 5.
5) Vehicles pass a particular point on a road at a rate of 51 per hour.
a) Give two reasons to support the use of the Poisson distribution as a suitable model for the number of vehicles passing this point.
Find the probability that in any randomly selected 10 minute interval:
b) exactly 6 cars pass this point,
c) at least 9 cars pass this point.
After the introduction of a roundabout some distance awat from this point it is suggested that the number of vehicles passing it has decreased. During a randomly selected 10 minute interval 4 vehicles pass this point.
d) Test, at the 5% level of significance, whether or not there is evidence to support the suggestion that the number of vehicles has decreased. State your hypotheses clearly.
6) From past records a manufacturer of ceramic plant pots knows that 20% of them will have defects. To monitor the production process, a random sample of 25 pots is checked eacg dat and the number of pots with defects is recorded.
a) Find the critical regions for a two-tailed test of the hypothesis that the probability that a plant pot has defects is 0.20. The probability of rejection in either tail should be as close as possible to 2.5%.
b) Write down the significance level of the above test.
A garden centre sells these plant pots at a rate of 10 per week. In an attempt to increase salses, the price was reduced over a six-week period. During this period a total of 74 pots was sold.
c) Using a 5% level of significance, test whether or not there is evidence that the rate of sales per week has increased during this six-week period.
Only need help with the last part of question 5.
5) Vehicles pass a particular point on a road at a rate of 51 per hour.
a) Give two reasons to support the use of the Poisson distribution as a suitable model for the number of vehicles passing this point.
Find the probability that in any randomly selected 10 minute interval:
b) exactly 6 cars pass this point,
c) at least 9 cars pass this point.
After the introduction of a roundabout some distance awat from this point it is suggested that the number of vehicles passing it has decreased. During a randomly selected 10 minute interval 4 vehicles pass this point.
d) Test, at the 5% level of significance, whether or not there is evidence to support the suggestion that the number of vehicles has decreased. State your hypotheses clearly.
6) From past records a manufacturer of ceramic plant pots knows that 20% of them will have defects. To monitor the production process, a random sample of 25 pots is checked eacg dat and the number of pots with defects is recorded.
a) Find the critical regions for a two-tailed test of the hypothesis that the probability that a plant pot has defects is 0.20. The probability of rejection in either tail should be as close as possible to 2.5%.
b) Write down the significance level of the above test.
A garden centre sells these plant pots at a rate of 10 per week. In an attempt to increase salses, the price was reduced over a six-week period. During this period a total of 74 pots was sold.
c) Using a 5% level of significance, test whether or not there is evidence that the rate of sales per week has increased during this six-week period.
Here's some goop;
Population - A collection of items
Sampling Frame -A list of items in a population
Census - A complete enumeration of a population
Sample - A selection of items from a population
Statistic - A random variable consisting of any function of the sample data that involves no other quantities
Null Hypothesis - The working hypothesis that is assumed true
Alternative Hypothesis - Describes situation if null is false
Test Statistic - Statistic used in hypothesis test
Sampling distribution - Distribution of a Statistic (e.g. binomial)
Critical Region - Range of values of a test statistic that would lead one to reject the null hypothesis
Significance level Used to determine critical region..it is the level of probability that one is willing to accept
Conditions for Binomial distribution
(1) Fixed number of trials
(2) Independent trials
(3) Either succeed or fail only
(4) Probability of success constant
Conditions for Poisson distribution
(1) Independent events
(2) Occur singly in time and space
(3) Events occur at a constant rate
A binomial distribution can be approximated by a poisson distribution if N is large and P is small
A binomial distribution can be approximated by a normal distribution if N is large, and both np and n(1-p) exceed 5
A poisson distribution can be approximated by a normal distribution if Y-N(λ , λ ) and λ>10
Continuous Uniform Distribution
E(X)= (a+b)/2
Var(X) = (b-a)ÂČ/12
where b and a are the upper and lower boundaries respectively
Population - A collection of items
Sampling Frame -A list of items in a population
Census - A complete enumeration of a population
Sample - A selection of items from a population
Statistic - A random variable consisting of any function of the sample data that involves no other quantities
Null Hypothesis - The working hypothesis that is assumed true
Alternative Hypothesis - Describes situation if null is false
Test Statistic - Statistic used in hypothesis test
Sampling distribution - Distribution of a Statistic (e.g. binomial)
Critical Region - Range of values of a test statistic that would lead one to reject the null hypothesis
Significance level Used to determine critical region..it is the level of probability that one is willing to accept
Conditions for Binomial distribution
(1) Fixed number of trials
(2) Independent trials
(3) Either succeed or fail only
(4) Probability of success constant
Conditions for Poisson distribution
(1) Independent events
(2) Occur singly in time and space
(3) Events occur at a constant rate
A binomial distribution can be approximated by a poisson distribution if N is large and P is small
A binomial distribution can be approximated by a normal distribution if N is large, and both np and n(1-p) exceed 5
A poisson distribution can be approximated by a normal distribution if Y-N(λ , λ ) and λ>10
Continuous Uniform Distribution
E(X)= (a+b)/2
Var(X) = (b-a)ÂČ/12
where b and a are the upper and lower boundaries respectively
Tindo
Chapter 4C, pg 103....qs 5...How do you do that?
X-B(20,0.50)
With 10% significance level in a two tailed test, that means basically 5% sig level in two lots of one tailed tests, above and below
=> P(x«7)= 0.1316 <---- too high, no rejection
=> P(x»7) = 1-P(x«6) = 0.9423 <------definitely no rejection
They write the answer in the back of the book as 0.2632 , so I guess that is just double the lowest probability.... o____0
Significance level Used to determine critical region..it is the level of probability that one is willing to accept
yep, I saw this on the S2 revision book, but it didnt make much sense to me, maybe it gets you the mark but does any one know how to phrase it in a more understandable way
yep, I saw this on the S2 revision book, but it didnt make much sense to me, maybe it gets you the mark but does any one know how to phrase it in a more understandable way
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