S2 FAQ Flashcards
Why have you used the CLT?
Parent distribution not known
How do you know T has a bigger variance than S?
S is more concentrated towards 0 therefore T has bigger variance
What happens to the probability of a Type II error as the sig level increases?
It decreases, an increased prob of Type I error means a decreased prob of Type II error. (CR larger)
What does the letter x represent in a probability density function?
Values taken by X (not an event that occurs)
What does it mean to ‘occur randomly’
Doesn’t occur at regular or predictable intervals.
Explain how to take a random sample
Obtain list, number (thing) sequentially, select using random numbers. Ignore repeats or numbers outside interval.
How must crystals be independent?
Crystals must occur independently of one another.
How to show the area is not finite?
After integrating state it gives an infinite answer
What does it mean to be independent?
The (position) of one doesn’t affect that of another (or the probability that another one does so)
What is u?
The population mean amount of …
What’s another way to say correlation doesn’t imply causation?
Can’t deduce cause and effect
Give an improved version of ‘the probability that T occurs is constant’
T is equally likely to take any value between a and b.
Where have you used the Central Limit Theorem?
In using normal tables/standardising/distribution of X
Why is contracting flu not Poisson?
It’s contagious so incidences don’t occur independently
When selecting a sample it’s required the same person isn’t selected twice, does this invalidate your calculation?
Binomial requires being chosen independently, which this isn’t, but that is unimportant as the population is large.
Why is a method of sampling where some numbers more likely to be chosen unsatisfactory?
Not all equally likely
What are three statistical properties of your survey which enable reliable conclusions about p to be drawn?
Members of population equally likely to be chosen, chosen independently/randomly, large sample
Why doesn’t a distribution of E~N mean you need CLT of Ē?
Distribution of E normal so that of Ē is normal.
Why is your answer (with unbiased estimates) only an estimate?
Variance is estimated
What properties of a method of sampling is needed to justify a binomial?
Selected independently, each person equally likely to be chosen.
As sample size increases what happens to the probability of a type II error?
It decreases.
A small number of people earn very high salaries, how does this affect the use of normal distribution
It is skewed so not symmetrical, therefore it is an inappropriate model
Why is the standard deviation of one greater than other probability density function?
It is more spread out
Conditions for binomial to Poisson?
n>50 np
Comment on ‘this sampling method must have been biased’
The method is unbiased, it’s not unlikely
Why do you need to assume it is normal?
CLT doesn’t apply as n is small so need to know distribution
Test >0.65 and
Same conclusion (insuf ev to reject/suf ev to reject) as test symmetric
Do you need an extra information to estimate P(Ē>10)?
No, CLT applies so can assume distribution is normal
State two conditions for X to be well modelled by a normal distribution
Distribution symmetric, no substantial truncation, unimodal/increasingly unlikely further from u
What is a random sample?
Each element equally likely to be selected (and all selections independent)
Why is choosing first few on list not a satisfactory sample method?
Biased as many people can’t be chosen.
Why are your normal answers only estimates?
Based on a sample
How to show it is a valid probability density function?
Integrate = 1 and state function non negative for all x in range.
