Statistics Year 1 Flashcards
Working with Data Probability Statistical Hypothesis Testing
What are mutually exclusive events?
Possible outcomes that cannot occur at the same time
P(A) + P(B)
What are independent events?
The first event occuring doesn’t affect the second event occuring
P(A) x P(B)
What is the notation for binomial distrobution?
X ~ B( n, p )
n = trial numbers
p = probability of success
x = number of times of succes
What are the conditions for binomial probability?
Independent events
Only two possible outcomes
Fixed probability
What is the formula for binomial distrobution?
In formula book
How do you calculate the following probabilities? P(x > k) P(x < k) P(x ≥ k) P(a ≤ x ≤ b)
P(x > k) = 1 - P(x ≤ k)
P(x < k) = P(x ≤ k-1)
P(x ≥ k) = 1- P(x ≤ k-1)
P(a ≤ x ≤ b) = P(x ≤ b-1) - P(x ≤ a)
What happend for x = 6 if you put this into you calculator?
Binomial PD
Binomial CD
Binomial PD P( x = 6)
Binomial CD P(x ≤ 6)
How do you set up a hypothesis test?
let p = probability of yellow car
H0: null hypothesis p = 0.4
H1: alternative hypothesis p < 0.4
significance level 5%
assume H0 let X = number who have yellow car
X ~ B(12, 0.4)
P(x ≤ 3) = 0.225
0.225 > 5%
p-value > sig value
Keep H0 as the evidence os not strong enought to reject H0 at the 5% significance level
How do you conduct a two tail test?
When H1: p ≠ 7
Divide significance level by two and test for that
What are critical regions?
Set of values which lead to rejecting H0 in favour of H1
What must a probability distrobution add up to?
1
What is a population?
Set of all the individuals in a hypothesis test
How do you calculate the variance and standard deviation?
Variance (σ²) - in formula book Standard deviation (σ) - square root variance
What is simple random sampling?
Every possible sample of size n is likley to be picked
Population choose n possibilities
e.g. 19 in population sample size 5 11628 possible samples
What is oppurtunity sampling?
Based on convenience
e.g. six closest to me
