Flashcards in Stats A level Deck (36)

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1

## What does the product moment correlation coefficient describe?

### The linear correlation (association) between two variables

2

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

###
H₀: p = 0

H₁: p > 0

or

H₀: p = 0

H₁: p < 0

3

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

###
H₀: p = 0

H₁: p ≠ 0

4

## What does the ∩ symbol mean?

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

5

## What does the ∪ symbol mean?

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

6

## What does the A' symbol mean?

### Complement: Eg, A' is everything NOT in A

7

## P(B|A) =

### P(B∩A)/P(A)

8

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

### 1

9

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

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

10

## Describe the normal distribution

###
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

11

##
What is the mean, and standard variation of the standard normal distribution?

How is the standard normal variable written?

###
mean = 0, standard deviation = 1

Z ~ N (0, 1²)

12

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

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

13

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

###
μ = np

σ = √np(1-p)

14

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

### Continuity correction

15

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

###
x̅ ~ N(μ, σ²/n)

(That is a capital X)

16

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

###
x̅ ~ N(μ, σ²/n)

Z ~ N (0, 1)

Z =( x̅ - μ )/ (σ/√n)

17

## How do you convert between Z value and X?

### Z = (X - μ) / σ

18

## What is the letter used for product moment correlation coefficient?

### r

19

## Describe the product moment correlation coefficient

###
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

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

### They might have a non-linear relationship

21

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

###
r = PMCC for sample

ρ (rho)= PMCC for a whole population

22

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

###
H₀: ρ = 0

H₁: ρ ≠ 0

23

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

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

24

##
What does this notation mean?

n(R) and P(R)

###
n(R) = The number of outcomes in the event R

P(R) = The probability that event R occurs

25

## Which values can a continuous random variable take?

### One of infinitely many values

26

## What shape is a normal distribution?

### bell-shaped

27

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

### About 68%

28

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

### About 95%

29

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

### About 99.7%

30