Stats- Prob, Distributions And Hypothesis Testing Flashcards
(26 cards)
What are key features of a normal distribution curve?
Mode=median=mean
Symmetrical
68% is within 1 SD
95% within 2 SD
99.7% within 3 SD
How do you state the normal distribution?
X ∼ N(𝝁, 𝝈𝟐)
Where 𝝁 is the population mean
𝝈𝟐 is the variance (SD squared)
What is the standard normal distribution? What is its equation?
Z~ B(0, 1*)
Z = (x-𝝁) / 𝝈
Where are the points of infection on a normal distribution curve?
+ or - 1 SD away from the mean
Where the gradient changes sign
How can you estimate the SD and mean on a normal distribution curve?
Use the range to get SD
{ 𝝁 - 3𝝈 < x < 𝝁 + 3𝝈}
Or estimate the mean and points of infection, then use
Point of inflection = 𝝁 + or - 𝝈
When can binomial distribution be estimated by the normal distribution?
What equations are used to do this?
When n>50 and p is close to 0.5
𝝁 = np
𝝈 = square root np(1-p)
What does all probability add up to?
1
How is binomial distribution stated?
X ~ N(n,p)
Where n is the number of trials and p is the probability
What are the four conditions for binomial distribution?
Each trial must be independent to the other
Probability remains constant
Fixed number of trials
Two outcomes (success and failure)
What is the equation for binomial distribution probability, without using a calc?
P(X=x) = nCx . P^x . (1-p)^n-x
What two equations can be used for 𝝁 and 𝝈? How do you test the validity of the calculated values?
𝝁 = np
𝝈 = square root np(1-p)
Compare values with the values from the calculator. If the values are the same/ very similar they are valid. If different- I shows any claims made are not supported or valid
What does P(A n B) mean?
Prob of getting A and B
What does P(A u B) mean?
Prob of getting A or B
What does it mean if probabilities are mutually exclusive? What is the equation to show this?
Means the probabilities have no common outcomes P(AnB) = 0
P(AuB) = P(A) + P(B)
What does it mean is probabilities are independent? What are the equations to show this?
Where the prob of one outcome does not affect the prob of another/ the next outcome
P(AnB) = P(A) x P(B)
What is the equation for when probabilities are not mutually exclusive?
P(AuB) = P(A) + P(B) - P(AnB)
How do you show conditional probability?
P(AIB)
What is meant by conditional probability? What is the equation to show if probabilities are conditional?
Where one probability occurs GIVEN another occurs
P(AIB) = P(A, given B)
P(AnB) = P(A) x P(BIA)
Describe how to answer a binomial hypothesis testing
Define x, and state x binomially
State H0 and H1
Calculate the expected value (np)
If actual number> np use a right hand tail
If actual number< np use a left hand tail
Us the tail to calculate the probability of the actual number
if p> signif level, accept H0
If p< signif level, fail to accept H0
What are the two options for H0 in hypothesis testing? What do they imply?
Accept- no signif evidence
Fail to accept- signif evidence
In hypothesis testing, what is the critical region, and what is the acceptance region?
The critical region is is a stat value falls In it, you fail to accept H0
The acceptance region is where any value accepts H0
In hypothesis testing, what is the critical value?
The first value to fall in the critical region, and fail to accept H0
How do you find the critical region on a binomial distribution graph? Using the significance level
Use the significance level and the tail to find the area TO THE LEFT. E.g if 0.1% signif level and right tailed, the area would be 1-0.1=0.9
Use the inverse function, so the calculator suggests a number
Test the number to find the area. If the area is not within the area (above or below depending on tail) test the next number (above or below)
This will be the critical value, and the critical region will be between the two values that you tested
After calculating the critical value and region, what will the actual significance level be?
The probability of getting the critical value
