chapter 18 - statistical hypothesis

Question 1

census

Answer 1

measures information about the entire population - all individuals of interest
- takes lots of time and cost - so more for larger organisations

Question 2

when is it impossible to carry out a census

Answer 2

• when it impossible to identify or get access to all members of a population eg all the ants in the world
• if the process of collecting data destroys the object being measured eg max load that can be placed on a shelf would mean breaking all shelves

Question 3

sample

Answer 3

only measured part of a population

Question 4

population parameter

Answer 4

a numerical characteristic of a population eg its mean variance

Question 5

simple random sampling

Answer 5

every possible sample has an equal chance of being selected eg random number generation all samples are equally as likely
+unbiased sample
- hard - need a list of the whole pop and everyone to respond
- time consuming and expensive

Question 6

opportunity sampling

Answer 6

sampling only from the individuals willing to take part - chasing respondents based on their availability and convenience
(non random)
+cheap and convenient
- may introduce bias and not be generalisable

Question 7

systematic sampling

Answer 7

taking participants at regular intervals from a list of the population (starting point is chosen at random)
+avoids unwanted clustering of data
+easier than using random no. generators
- needs a list of whole pop
- less random as no longer independent

Question 8

stratified sampling

Answer 8

splitting the population into groups based on factors relevant to the research then random sampling from each group in proportion to the size of that group
+sample is representative of the factors
- needs list of whole pop with info about each member
- time consuming and expensive
- determining factors is not always obvious

Question 9

quota sampling

Answer 9

splitting the population into groups based on relevant factors then opportunity sampling from each group until a required no. participants are found
(non random)
+ensures sample is representative over the factors identified
- may introduce bias and not be generalisable

Question 10

cluster sampling

Answer 10

splitting the pop into clusters based on convenience then randomly choosing clusters to study further
+cheaper and easier
- less accurate - clusters may be non representative

Question 11

lower tail test

Answer 11

take H1 as p<
and use P(X<=

Question 12

upper tail test

Answer 12

take H1 as p>
and use P(X>= x) so have to do 1-P(X<=x-1)

Question 13

two tailed

Answer 13

take H1 as p =/=
if they tell you that 45 / 100 people have a car and the question is if it has changed from 36% having a car you use P(X >= 45) as 45% > 36% so use the upper tail and halve the sugificance value when you are using it

Question 14

hypothesis test answers layout

Answer 14

• define rV X
• distribution assumed (define p) - X~B(n,p)
• H0 and H1 =
• rejection criteria
• test statistic - P(X <=
• P value =
• conclusion (sufficient evidence to reject H0?)
• context (means there is sufficient evidence to suggest…)

Question 15

critical value/ region

Answer 15

to have succulence evidence to reject H0 there would need to be x or fewer
x = critical value
critical region is X <= x
acceptance region is X >= x+ 1
use binomial CD list

Question 16

prob of incorrectly rejecting H0

Answer 16

is the prob of the test statistic being in the critical region

Question 17

critical region 2 tailed test

Answer 17

use binomial CD list again but the critical region will be like reject H0 if X<= 5 or X >=30