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OCR A level Maths > Stats Year 1 > Flashcards

Stats Year 1 Flashcards

1
Q

What are the 5 things that must be in a hypothesis testing

A
  • Null hypothesis
  • Alternative hypothesis
  • Test statistic
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2
Q

Define the significance level

A

The probability of incorrectly rejecting the null hypothesis

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3
Q

Define a population

A

The whole set of items that are of interest

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4
Q

Define census

A

Observes or measures every member of a population

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5
Q

Define sample

A

A selection of observations taken from a subset of the population which is used to find out information about the population as a whole

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6
Q

Define sampling units

A

Individual units of a population

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7
Q

What is a sampling frame

A

Sampling units of a population that are individually named or numbered to form a list

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8
Q

What is an advantage of a census

A

It should give a completely accurate result

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9
Q

What are the 3 disadvantages of a census

A
  • Time consuming and expensive
  • Cannot be used when the testing process destroys the item
  • Hard to process large quantity of data
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10
Q

What are the 3 advantages of using a sample

A
  • Less time consuming and expensive than a census
  • Fewer people have to respond
  • Less data to process than in a census
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11
Q

What are the 2 disadvantages of using a sample

A
  • The data may not be as accurate
  • The sample may not be large enough to give information about small sub-groups of the population
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12
Q

What is a simple random sample

A

Where every sample has an equal chance of being selected

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13
Q

How do you carry out a simple random sample

A
  • Allocate each person or thing in the sampling frame a unique number
  • Random number generate
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14
Q

What is systematic sampling

A

Required elements are chosen at regular intervals from an ordered list e.g. every 5 numbers are selected

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15
Q

What is stratified sampling

A

The population is divided into mutually exclusive strata (males and females for example) and a random sample is taken from each

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16
Q

What is the equation to calculate how many people/things should be involved in the sample per strata in stratified sampling

A

Number in stratum/ number in population then x by overall sample size

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17
Q

What are the 3 advantages of simple random sampling

A
  • Free of bias
  • Easy and cheap to implement for small populations and small samples
  • Each sampling unit has a known and equal chance of selection
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18
Q

What are the 2 disadvantages of simple random sampling

A
  • Not suitable when the population size or the sample size is large n
  • A sampling frame is needed
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19
Q

What are the 2 advantages of systematic sampling

A
  • Simple and quick to use
  • Suitable for large samples and large populations
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20
Q

What are the 2 disadvantages of systematic sampling

A
  • A sampling frame is needed
  • It can introduce bias if the sampling frame is not random
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21
Q

What are the 2 advantages of stratified sampling

A
  • Sample accurately reflects the population structure
  • Guarantees proportional representation of groups within a population
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22
Q

What are the 2 disadvantages of stratified sampling

A
  • Population must be clearly classified into distinct strata
  • Selection within each stratum suffers from the same disadvantages as simple random sampling
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23
Q

What is quota sampling

A

An interviewer or researcher selects a sample that reflects the characteristics of the whole population

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24
Q

What is opportunity sampling

A

Consists of taking the sample from people who are available at the time the study is carried out and who fit the criteria you are looking for

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25
Q

What are the 4 advantages of quota sampling

A
  • Allows a small sample to still be representative of the population
  • No sampling frame required
  • Quick, easy and inexpensive
  • Allows for easy comparison between different groups within a population
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26
Q

What are the 4 disadvantages of quota sampling

A
  • Non-random sampling can introduce bias
  • Population must be divided into groups, which can be costly or inaccurate
  • Increasing scope of study increases number of groups, which adds time and expense
  • Non-responses are no recorded as such
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27
Q

What are the 2 advantages of opportunity sampling

A
  • Easy to carry out
  • Inexpensive
28
Q

What are the 2 disadvantages of opportunity sampling

A
  • Unlikely to provide a representative sample
  • Highly dependent on individual researcher
29
Q

What are variables that are associated with numerical observations called

A

Quantitative variables

30
Q

What are variables associated with non-numerical observations called

A

Qualitative variables

31
Q

What is a continuous variable

A

A variable that can take any value in a given range

32
Q

What is a discrete variable

A

A variable that can take only specific values in a given range

33
Q

What is the mode

A

Value that occurs the most

34
Q

What is the median

A

The middle value

35
Q

How do you calculate the variance

A

Mean of the squares minus the square of the mean

36
Q

How do you calculate standard deviation from the variance

A

Square root it

37
Q

What are the 3 common definitions of an outlier if not stated in the question

A
  • Upper quartile + 1.5(IQR)
  • Lower quartile - 1.5(IQR)
  • The mean plus or minus 2 standard deviation
38
Q

The process of what is known as cleaning the data

A

Process of removing anomalies from a data set

39
Q

How do you calculate the frequency density

A

Frequency/ class width

40
Q

When comparing data what 2 things must you compare

A
  • A measure of location
  • A measure of spread
41
Q

What things are measures of location

A
  • Mode
  • Mean
  • Median
  • Quartiles
  • Percentiles
42
Q

What things are measures of spread

A
  • Range
  • Interquartile range
  • Variance
  • Standard deviation
43
Q

What are the 5 possible correlation descriptions

A
  • Strong negative correlation
  • Weak negative correlation
  • No correlation
  • Weak positive correlation
  • Strong positive correlation
44
Q

Is the explanatory variable dependent or independent

A

Independent

45
Q

Where does the explanatory variable go, x or y axis

A

x axis

46
Q

Is the response variable dependent or independent

A

Independent

47
Q

Which axises should you plot the response variable

A

Y-axis

48
Q

What type of relationships do the variables have if a change in one causes a change in the other

A

Casual relationship

49
Q

What is the equation of a regression line

A

y=a+bx

50
Q

What is an experiment

A

A repeatable process that gives rise to a number of outcomes

51
Q

What is an event

A

A collection of one or more outcomes

52
Q

What is a sample space

A

The set of all possible outcomes

53
Q

What is the term used to describe when events have no outcomes in common

A

Mutually exclusive

54
Q

For mutually exclusive events, how do you calculate the P(A+B)

A

P(A)+P(B)

55
Q

For independent events, how do you calculate P(AandB)

A

P(A) X P(B)

56
Q

How do you calculate whether events are independent

A

P(AandB) = P(A) X P(B)

57
Q

How do you calculate whether events are mutually exclusive

A

P(AandB) = P(A) + P(B)

58
Q

When using the binomial distribution function on your calculator using CD, what must you remember it is calculating

A

Equal to or less than the number (the x)

59
Q

What is the basic equation for binomial distribution

A

B(n,p)
- n= number of trials
-p= probability

60
Q

What is the null hypothesis

A

The hypothesis that you assume to be correct

61
Q

What is the alternative hypothesis

A

Tells you about the parameter if your assumption is shown to be wrong

62
Q

When dealing with a 2-tailed test, what happens to the signifance level

A

It is split in half, half of the percentage is given to below the number and the other half is given to above the number
e.g. for a 5% significance level 2.5% is given to above and 2.5% is given to below

63
Q

What is the rejection/ critical region

A

The region of the probability that would cause you to reject the null hypothesis

64
Q

What is the critical value

A

The first value to fall inside the rejection region

65
Q

What is the actual significance level

A

The probability of incorrectly rejecting the null hypothesis, the significance level given in the question is rarely the exact % you find from the calculator
- Say the question gives a 5% significance level, and the value given you 4.4% instead of exactly 5% the actual significance level is 4.4%

66
Q

How many rejections regions are there in a 2-tailed test

A

2, one at each end of the distribution

OCR A level Maths (2 decks)

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