Stats A level Flashcards
What does the product moment correlation coefficient describe?
The linear correlation (association) between two variables
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
General hypothesis testing: What is the null hypothesis and the alternative hypothesis for a two tailed test?
H₀: p = 0
H₁: p ≠ 0
What does the ∩ symbol mean?
Intersection: Eg. A ∩ B is the area that is in both A AND B
What does the ∪ symbol mean?
Union: Eg, A ∪ B is the area in A OR B
What does the A’ symbol mean?
Complement: Eg, A’ is everything NOT in A
P(B|A) =
P(B∩A)/P(A)
What is the area under a continuous probability curve equal to?
1
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
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
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)
When can the binomial distribution be approximated by a normal distribution?
If n is large (>50) and p is close to 0.5.
When using the normal distribution to approximate the binomial distribution, what is the mean and standard deviation?
μ = np σ = √np(1-p)
What do you need to apply when calculating probabilities, using a normal distribution to approximate a binomial distribution?
Continuity correction
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
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)
How do you convert between Z value and X?
Z = (X - μ) / σ
What is the letter used for product moment correlation coefficient?
r
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
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
What are the letters used in a product moment correlation coefficient hypothesis test?
r = PMCC for sample
ρ (rho)= PMCC for a whole population
Write down the null and alternative hypothesis for a two tailed PMCC test?
H₀: ρ = 0
H₁: ρ ≠ 0
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
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
Which values can a continuous random variable take?
One of infinitely many values
What shape is a normal distribution?
bell-shaped
How much data lies within one standard deviation of the mean?
About 68%
How much data lies within two standard deviations of the mean?
About 95%
How much data lies within three standard deviations of the mean?
About 99.7%
Where are the points of inflection on a normal distribution?
μ ± σ
What is another way of writing P(Z<a></a>
Φ(a)
When can you approximate the binomial distribution with the normal distribution?
When n is large (>50) and the probability is close to 0.5
Why is the normal approximation only valid when the probability is close to 0.5?
Because normal distribution is symmetrical
It can be assumed that all normally distributed data lies within n standard deviations of the mean? What number is n?
5
eg, all the data is within μ ± 5σ
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?
No, they are approximations, for any calculations, use the calculator values
Can be used to show that data is normally distributed
What is the critical region?
The set of all values of the test statistic for which the null hypothesis is rejected in a hypothesis test
