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Maths > Correlation And Hypothesis Testing > Flashcards

Correlation And Hypothesis Testing Flashcards

1
Q

What type of correlation is the PMCC is close to 1?

A

Positive linear correlation

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2
Q

What type of correlation if the PMCC is close to -1?

A

Negative linear Negative linear

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3
Q

What does r mean (hypothesis testing)?

A

PMCC for a sample

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4
Q

What does p mean (hypothesis testing)?

A

PMCC for the whole population

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5
Q

“Test for a positive correlation”
Which tail do you use?

A

Positive (upper) one tailed

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6
Q

“Evidence for some correlation” “No evidence for some correlation”
What tailed is used?

A

Two tailed (half the significance level)

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7
Q

Hypothesis for negative (lower) one tail

A

HO: p = 0
H1: p < 0
(PMCC: If the value given is smaller than the negative value from the table, reject H0 so there’s enough evidence)

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8
Q

“Test for a negative correlation”
What tailed is used?

A

Negative (lower) one tail

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9
Q

Hypothesis for positive (upper) one tail

A

H0: p = 0
H1: p > 0
(PMCC: If the value given is larger than the value from the table, reject H0 so there’s enough evidence)

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10
Q

Hypothesis for some correlation two tail

A

H0: p = 0
H1: p ≠ 0
(PMCC if neg value from table < r > value from table, reject H0 so there’s enough evidence)

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11
Q

To find the critical value

A

Use PMCC table

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12
Q

If the value is within the critical region…

A

It’s significant meaning you reject H0 so there’s enough evidence to suggest there’s a neg correlation/pos correlation/some correlation/an increase/a decrease etc

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13
Q

Test statistic

A

Used to test the hypothesis. It could be the result of the experiment calculated from the exampple

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14
Q

Null hypothesis H0

A

Hypothesis you assume to be correct

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15
Q

Alternate hypothesis

A

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

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16
Q

Hypothesis test

A

A statement made about the value of a population parameter. It uses a sample to determine whether to reject H0

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17
Q

Critical value

A

The first value to fall inside the critical region

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18
Q

Critical regions

A

A region of the probability distribution which, if the test statistic falls within, you reject the null

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19
Q

Acceptance region

A

The area in which we accept the null hypothesis

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20
Q

“Test for an increase/improvement in…”
Which tail is used?

A

Upper one tail

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21
Q

“Test for a decrease/an over-estimate….”
Which tail is used?

A

Lower one tail

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22
Q

“Test for a change in….”
Which tail is used?

A

Two tailed

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23
Q

PMCC on calculator (from a given table)

A
  1. Menu 6
  2. 2
    3 .Type values
  3. Optn
  4. 4
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24
Q

Critical value on calculator

A
  1. Menu 7
  2. Scroll down 1
  3. 2 (for testing whether a given variable is significant), 1 (for finding the critical region)
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25
Q

When to use binomial or cumulative probability?

A

Binomial P(X = 4)
Cumulative P(X<4) P(X≤4) etc

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26
Q

Binomial distribution/probability

A
  1. Menu 7
  2. 1
  3. 2
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27
Q

Cumulative probability

A

Use table

  1. Menu 7
  2. Scroll opt 1
  3. 2 (testing a variable)
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28
Q

Comment on the suitability of the binomial distribution model

A

The probability is lower/higher than the expected value which suggests the model is not accurate

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29
Q

Suggest one improvement for the distribution model

A

A non uniform distribution

30
Q

Requirements of a binomial distribution

A

1: The number of observations n is fixed.
2: Each observation is independent.
3: Each observation represents one of two outcomes (“success” or “failure”
4) there is fixed probability

31
Q

Requirements of a normal distribution

A

1) The mean, median and mode are exactly the same.
2) The distribution is symmetric about the mean—half the values fall below the mean and half above the mean.
3) The distribution can be described by two values: the mean and the standard deviation.

32
Q

Finding mean from binomial distribution

A

np

33
Q

Finding variance from binomial distribution

A

np(1-p)
If 1-p is negative the just use np

34
Q

Later it was discovered that the local scout group visited the supermarket that afternoon to buy food for their camping trip.
(f) Comment on the validity of the model used to obtain the answer to part (e), giving a reason for your answer

A

The 20 customers are independent & the members of the scout group may invalidate this so binomial distribution would not be valid

35
Q

When testing a value against a hypothesis to see if there’s change/improvement.

A
  • decrease P(X<_8)
  • change/increase P(X>_8)
36
Q

P value for two tailed test

A

Times the probability by 2

37
Q

PMCC measures…

A

how strong the correlation between two variables is.

38
Q

Z for normal distribution

A

X-U/o

39
Q

_
X ~ N

A

(u, (o/root)^2

40
Q

Normal distributions

A

X~N (u, o^2)

41
Q

Normal distribution significant figures

A
  • table = 4 d.p
  • calculator = 3 d.p
    (State whether your using a table or calculator)
42
Q

Standard normal distribution

A

Z~N (0.1)^2
Z=X-u/o

43
Q

Normal to standard

A

X~B (50, 4^2)
P(X<53)
P(Z<53-50/4) = P (Z<0.75)
0(0.75)

44
Q

The Central Limit Theorem

A

Can use mean full time and mean part time ~ Normal

45
Q

State an assumption you’ve used (when using variance)

A

Variance of sample = variance of pop.

46
Q

Text whether or not there is evidence that the PMCC is positive

A

Positive upper tail

47
Q

Two condition under which the normal distribution may be used as an approximation to the binomial distribution

A

Number of trials is large and probability of success is close to
0.5

48
Q

If differences in mean is greater than differences in standard deviation

A

Sizes of standard deviations are small compared with the difference in mean temperatures making it more likely that the difference in means is significant

49
Q

Explain why it is reasonable to model the daily mean pressure for Beijing, during
May to August using a normal distribution.

A

It’s bell shaped

50
Q

give a reason why we cannot say there is no chance of a hurricane in Beijing during May to August.

A

The tails of a Normal distribution are infinite.

51
Q

When to use upper and lower bounds for distribution values?

A

Only when using np, np(1-p)

52
Q

How to show that the distribution of T is not discrete uniform distribution?

A

Show that the probabilities of the outcome aren’t equal

53
Q

y=ax^n

A

logy=loga+nlogx

54
Q

Y=ab^x

A

Logy=loga+xlogb

55
Q

State, giving a reason, whether or not the correlation coefficient is consistent with Tess’a suggestion

A

Since r is close to -1 it is consistent (ie has strong correlation)

56
Q

The linear regression equation is w 10 755- 171 t. Give an interpretation of the gradient of this regression equation

A

As t increases, w decrease

57
Q

Subjects have a negative correlation. Given that on a day the humidity was high, what would expect the No. hours of sunshine to be?

A

Lower than average

58
Q

Explain why this normal distribution may not be good model for T?

A

The model suggests non-negligible profitability of T values < 0 which is impossible

59
Q

Give an interpretation of the correlation

A

Analyse the correlation using the variables

60
Q

When to use (np, square root np(1-p))

A

When asks for suitable approximation or normal approximation

61
Q

What data should be used when asked about ‘typical’ or ‘average’?

A

Mean and median (location of the data)

62
Q

What data to use when asked about how ‘spread out’ the data is?

A
  • Calculate standard deviation, range & interquartile range
  • describe variability of the data
63
Q

Describe the shape of the data

A
  • how many peaks or modes
  • symmetric or asymmetric
  • skew (is there a long tail to the left or right)
64
Q

What type of distribution do we have a sample of data?

A

frequency distribution

65
Q

What type of distribution do we have the entire population?

A

Probability distribution

66
Q

Relationship between mean and median regarding symmetry

A

If it’s symmetric, we can expect the mean and median to be about the same

67
Q

What is unimodal?

A

One peak

68
Q

Examples of variables that are positively skewed

A

Waiting times
Household income

69
Q

Examples of variables that are negatively skewed

A

Satisfaction measures
Retirement age

70
Q

Examples of variables that are symmetric

A

Height
Weight

71
Q

When is poisson distribution used?

A
  • to describe rare events & discrete occurrences over an interval of time
  • independent (in non overlapping intervals)
  • the range is form 0 onwards
  • constant expected no. occurence
72
Q

Examples of when poisson distribution would be used

A
  • no. random arrivals per some time interval (customers arrivals to a store on weekday mornings)
  • queuing theory
  • rare blood disease

Maths (5 decks)

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