Brainscape's Knowledge GenomeTM

Browse over 1 million classes created by top students, professors, publishers, and experts.


See full index

A Level Maths > Stats A level > Flashcards

Stats A level Flashcards

1
Q

What does the product moment correlation coefficient describe?

A

The linear correlation (association) between two variables

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
2
Q

General hypothesis testing: What is the null hypothesis and the alternative hypothesis for a one tailed test?

A 
H₀: p = 0
H₁: p > 0
or
H₀: p = 0
H₁: p < 0
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
3
Q

General hypothesis testing: What is the null hypothesis and the alternative hypothesis for a two tailed test?

A

H₀: p = 0

H₁: p ≠ 0

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
4
Q

What does the ∩ symbol mean?

A

Intersection: Eg. A ∩ B is the area that is in both A AND B

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
5
Q

What does the ∪ symbol mean?

A

Union: Eg, A ∪ B is the area in A OR B

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
6
Q

What does the A’ symbol mean?

A

Complement: Eg, A’ is everything NOT in A

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
7
Q

P(B|A) =

A

P(B∩A)/P(A)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
8
Q

What is the area under a continuous probability curve equal to?

A

1

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
9
Q

What is the distribution of X, if it is normally distributed?

A

X ~ N(μ, σ²) where μ is the population mean, and σ² is the population variance

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
10
Q

Describe the normal distribution

A

1) μ is the population mean, and σ² is the population variance
2) symmetrical (mean=median=mode)
3) Bell-shaped curve with asymptotes at each end
4) Total area under curve = 1
5) Point of inflection at μ+σ and μ-σ

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
11
Q

What is the mean, and standard variation of the standard normal distribution?
How is the standard normal variable written?

A

mean = 0, standard deviation = 1

Z ~ N (0, 1²)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
12
Q

When can the binomial distribution be approximated by a normal distribution?

A

If n is large (>50) and p is close to 0.5.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
13
Q

When using the normal distribution to approximate the binomial distribution, what is the mean and standard deviation?

A 
μ = np
σ = √np(1-p)
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
14
Q

What do you need to apply when calculating probabilities, using a normal distribution to approximate a binomial distribution?

A

Continuity correction

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
15
Q

For a random sample of size n taken from a random variable X ~ N(μ, σ²) , how is the sample mean normally distributed?

A

x̅ ~ N(μ, σ²/n)

That is a capital X

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
16
Q

What does Z= equal? (Combining the normal distribution of a sample mean, and Z values)

A

x̅ ~ N(μ, σ²/n)
Z ~ N (0, 1)
Z =( x̅ - μ )/ (σ/√n)

17
Q

How do you convert between Z value and X?

A

Z = (X - μ) / σ

18
Q

What is the letter used for product moment correlation coefficient?

A

r

19
Q

Describe the product moment correlation coefficient

A

It describes the linear correlation between two variables
It can take the value between -1 (perfect negative correlation) and 1 (perfect positive correlation)
If r = 0 then there is no linear correlation

20
Q

Suggest a reason why two variables could still have a relationship but have a product moment correlation coefficient of zero

A

They might have a non-linear relationship

21
Q

What are the letters used in a product moment correlation coefficient hypothesis test?

A

r = PMCC for sample

ρ (rho)= PMCC for a whole population

22
Q

Write down the null and alternative hypothesis for a two tailed PMCC test?

A

H₀: ρ = 0

H₁: ρ ≠ 0

23
Q

How do you complete a hypothesis test for product moment correlation coefficient? Calculator or table?

A

You have to use the calculated values in the table in the back of the formula booklet

24
Q

What does this notation mean?

n(R) and P(R)

A 
n(R) = The number of outcomes in the event R
P(R) = The probability that event R occurs
25
Q

Which values can a continuous random variable take?

A

One of infinitely many values

26
Q

What shape is a normal distribution?

A

bell-shaped

27
Q

How much data lies within one standard deviation of the mean?

A

About 68%

28
Q

How much data lies within two standard deviations of the mean?

A

About 95%

29
Q

How much data lies within three standard deviations of the mean?

A

About 99.7%

30
Q

Where are the points of inflection on a normal distribution?

A

μ ± σ

31
Q

What is another way of writing P(Z<a></a>

A

Φ(a)

32
Q

When can you approximate the binomial distribution with the normal distribution?

A

When n is large (>50) and the probability is close to 0.5

33
Q

Why is the normal approximation only valid when the probability is close to 0.5?

A

Because normal distribution is symmetrical

34
Q

It can be assumed that all normally distributed data lies within n standard deviations of the mean? What number is n?

A

5

eg, all the data is within μ ± 5σ

35
Q

Can you use the percentage approximations (eg. about 68% of the data lies with 1 standard deviation of the mean) to calculate values for the μ or σ? What else would you use it for?

A

No, they are approximations, for any calculations, use the calculator values
Can be used to show that data is normally ditributed

A Level Maths (8 decks)

Brainscape helps you reach your goals faster, through stronger study habits.
© 2024 Bold Learning Solutions. Terms and Conditions