Stats A level

Question 1

What does the product moment correlation coefficient describe?

Answer 1

The linear correlation (association) between two variables

Question 2

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

Answer 2

H₀: p = 0
H₁: p > 0
or
H₀: p = 0
H₁: p < 0

Question 3

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

Answer 3

H₀: p = 0

H₁: p ≠ 0

Question 4

What does the ∩ symbol mean?

Answer 4

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

Question 5

What does the ∪ symbol mean?

Answer 5

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

Question 6

What does the A’ symbol mean?

Answer 6

Complement: Eg, A’ is everything NOT in A

Question 7

P(B|A) =

Answer 7

P(B∩A)/P(A)

Question 8

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

Answer 8

1

Question 9

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

Answer 9

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

Question 10

Describe the normal distribution

Answer 10

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

Question 11

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

Answer 11

mean = 0, standard deviation = 1

Z ~ N (0, 1²)

Question 12

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

Answer 12

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

Question 13

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

Answer 13

μ = np
σ = √np(1-p)

Question 14

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

Answer 14

Continuity correction

Question 15

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

Answer 15

x̅ ~ N(μ, σ²/n)

That is a capital X

Question 16

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

Answer 16

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

Question 17

How do you convert between Z value and X?

Answer 17

Z = (X - μ) / σ

Question 18

What is the letter used for product moment correlation coefficient?

Answer 18

r

Question 19

Describe the product moment correlation coefficient

Answer 19

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

Question 20

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

Answer 20

They might have a non-linear relationship

Question 21

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

Answer 21

r = PMCC for sample

ρ (rho)= PMCC for a whole population

Question 22

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

Answer 22

H₀: ρ = 0

H₁: ρ ≠ 0

Question 23

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

Answer 23

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

Question 24

What does this notation mean?

n(R) and P(R)

Answer 24

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

Question 25

Which values can a continuous random variable take?

Answer 25

One of infinitely many values

Question 26

What shape is a normal distribution?

Answer 26

bell-shaped

Question 27

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

Answer 27

About 68%

Question 28

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

Answer 28

About 95%

Question 29

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

Answer 29

About 99.7%

Question 30

Where are the points of inflection on a normal distribution?

Answer 30

μ ± σ

Question 31

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

Answer 31

Φ(a)

Question 32

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

Answer 32

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

Question 33

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

Answer 33

Because normal distribution is symmetrical

Question 34

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

Answer 34

5

eg, all the data is within μ ± 5σ

Question 35

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?

Answer 35

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

Question 36

What is the critical region?

Answer 36

The set of all values of the test statistic for which the null hypothesis is rejected in a hypothesis test