S2 FAQ

Question 1

Why have you used the CLT?

Answer 1

Parent distribution not known

Question 2

How do you know T has a bigger variance than S?

Answer 2

S is more concentrated towards 0 therefore T has bigger variance

Question 3

What happens to the probability of a Type II error as the sig level increases?

Answer 3

It decreases, an increased prob of Type I error means a decreased prob of Type II error. (CR larger)

Question 4

What does the letter x represent in a probability density function?

Answer 4

Values taken by X (not an event that occurs)

Question 5

What does it mean to ‘occur randomly’

Answer 5

Doesn’t occur at regular or predictable intervals.

Question 6

Explain how to take a random sample

Answer 6

Obtain list, number (thing) sequentially, select using random numbers. Ignore repeats or numbers outside interval.

Question 7

How must crystals be independent?

Answer 7

Crystals must occur independently of one another.

Question 8

How to show the area is not finite?

Answer 8

After integrating state it gives an infinite answer

Question 9

What does it mean to be independent?

Answer 9

The (position) of one doesn’t affect that of another (or the probability that another one does so)

Question 10

What is u?

Answer 10

The population mean amount of …

Question 11

What’s another way to say correlation doesn’t imply causation?

Answer 11

Can’t deduce cause and effect

Question 12

Give an improved version of ‘the probability that T occurs is constant’

Answer 12

T is equally likely to take any value between a and b.

Question 13

Where have you used the Central Limit Theorem?

Answer 13

In using normal tables/standardising/distribution of X

Question 14

Why is contracting flu not Poisson?

Answer 14

It’s contagious so incidences don’t occur independently

Question 15

When selecting a sample it’s required the same person isn’t selected twice, does this invalidate your calculation?

Answer 15

Binomial requires being chosen independently, which this isn’t, but that is unimportant as the population is large.

Question 16

Why is a method of sampling where some numbers more likely to be chosen unsatisfactory?

Answer 16

Not all equally likely

Question 17

What are three statistical properties of your survey which enable reliable conclusions about p to be drawn?

Answer 17

Members of population equally likely to be chosen, chosen independently/randomly, large sample

Question 18

Why doesn’t a distribution of E~N mean you need CLT of Ē?

Answer 18

Distribution of E normal so that of Ē is normal.

Question 19

Why is your answer (with unbiased estimates) only an estimate?

Answer 19

Variance is estimated

Question 20

What properties of a method of sampling is needed to justify a binomial?

Answer 20

Selected independently, each person equally likely to be chosen.

Question 21

As sample size increases what happens to the probability of a type II error?

Answer 21

It decreases.

Question 22

A small number of people earn very high salaries, how does this affect the use of normal distribution

Answer 22

It is skewed so not symmetrical, therefore it is an inappropriate model

Question 23

Why is the standard deviation of one greater than other probability density function?

Answer 23

It is more spread out

Question 24

Conditions for binomial to Poisson?

Answer 24

n>50 np

Question 25

Comment on ‘this sampling method must have been biased’

Answer 25

The method is unbiased, it’s not unlikely

Question 26

Why do you need to assume it is normal?

Answer 26

CLT doesn’t apply as n is small so need to know distribution

Question 27

Test >0.65 and

Answer 27

Same conclusion (insuf ev to reject/suf ev to reject) as test symmetric

Question 28

Do you need an extra information to estimate P(Ē>10)?

Answer 28

No, CLT applies so can assume distribution is normal

Question 29

State two conditions for X to be well modelled by a normal distribution

Answer 29

Distribution symmetric, no substantial truncation, unimodal/increasingly unlikely further from u

Question 30

What is a random sample?

Answer 30

Each element equally likely to be selected (and all selections independent)

Question 31

Why is choosing first few on list not a satisfactory sample method?

Answer 31

Biased as many people can’t be chosen.

Question 32

Why are your normal answers only estimates?

Answer 32

Based on a sample

Question 33

How to show it is a valid probability density function?

Answer 33

Integrate = 1 and state function non negative for all x in range.