stuff to remember

Question 1

what do you do when the sample size is at least a tenth of the population

Answer 1

when n/N > 0.1, the variance is the usual thing ([➰^2]/n) times the finite population correction factor (1-[n/N])

N being provided in the exam is a suggestion that this is needed

Question 2

Bias formula

Answer 2

Bias(estimator) = E(estimator) - thing the estimator estimates
it’s positively biased if the bias is positive
(same for negative)

Question 3

how do you tell which estimator is better than another

Answer 3

the one with the smallest mean squared error is best

MSE(🌐)= Var(🌐) + (Bias (🌐))^2

Question 4

formula for confidence intervals

Answer 4

sample mean +- estimated standard error x t

Question 5

when determining which sample size will give a particular tolerance or confidence interval, which value of t do you use

Answer 5

the z value (t infinity), a/2

a/2 is used with all confidence interval questions and two tailed tests

a is used for one tailed tests

Question 6

when to use t n-1 and when to use z (t infinity) for confidence intervals and hypothesis testing

Answer 6

use t n-1 for:
• only means (never proportions)
• when n<30 AND v is unknown (so you’re given or made to work out the SAMPLE v rather than the v for the whole population)
• differences between two means WHEN variances ARE the same and UNKNOWN (and you have to use a pooled s from the formula sheet (both ns-2 instead of n-1)
• paired data (when you do d=x-y)

use t infinity or z for:
• proportions
• means where n is large and/or ➰is known
• finding n for a confidence interval (always)
• differences between two means UNLESS variances are unknown and equal (even if they’re unknown and unequal)

Question 7

which error is which

Answer 7

type 1: alpha, false positive, rejecting the null hypothesis when the null hypothesis is true (the worse one)

type 2: beta, false negative, accepting the null hypothesis when it isn’t true (the better one)

Question 8

what’s a probability distribution and what’s a probability function

Answer 8

function is the { thing

distribution is the table

Question 9

what is a binomial distribution

Answer 9

values come from a series of independent bernoulli trials so:

2 possible outcomes from each trial (success and failure)
fixed prob of success
fixed no of trials
trials independent

X~Bin(n,pi)

Question 10

what is a poission distribution

Answer 10

a discrete distribution where values are independent of each other and can occur anywhere on a continuum

X~Pois(lambda)

Question 11

What assumptions may you make when doing confidence intervals

Answer 11

1. samples are independent
2. values are normally distributed
3. when sample sizes are small and the variances unknown, they may be assumed to be equal

Question 12

Axioms of probability

Answer 12

1. a probability must be equal to or greater than zero
2. the probability of s, where s represents a set, is 1
3. the probability of a union of mutually exclusive events is the sum of their probabilities

Question 13

what is a p value

Answer 13

probability of obtaining a certain value, or something more extreme, if the null hypothesis is true

(the probability of making a type 1 error/false positive)❓

Question 14

when do you use the poisson approximation to the binomial

Answer 14

when n is so big that nCx doesn’t work,

when
n>30
n(pi) <10 because pi is so extremely small

Question 15

what is the power of a hypothesis test?

Answer 15

the probability that a false null hypothesis will be rejected

1-(probability null hypothesis will be rejected when it’s actually true)

= 1-p(type 2 error)
= 1-beta