Probability
When do you use a tree diagram?
When the given probabilities are conditional
Ex: cancer IF test positive
P1 does not equal P2
How do you find the mean of a discrete random variable?
mu = summation of x * p(x)
Where is the randomization distribution centered at?
the null
what is a discrete random variable?
a random variable is discrete if it has a finite set of possible values. for example possible answers can only be (1,2,3,4,...)
How do you know if two events are disjoint?
If only one of the two events can happen. P(A or B) = P(A) +P(B). they can't happen together
Name the two types of errors and what happens in both
Type 1 error- reject the null when its true (false positive)
Type 2 error - fail to reject the null when its false (false negative)
How do you find the standard deviation for a discrete random variable?
standard deviation= the square root of (summation[x-mean]^2 * p(x))
(n/k)= n!/k!(n-k)!
n is the total number of trials while k is the successes n-k would be failures
What is a sample statistic and how do you find a sample statistic?
If the question talks about means/averages find the sample means, if the question talks about proportions find the sample proportions from given data
What is the probability that a randomly selected person will drive a sports car?
84/240
2. We did not find any statistical conclusions, our test is inconclusive
What is the equation of the compliment of P(A) aka P(notA)
1-P(A)
What three things do you need for a binomial?
the number of trials,n, need to be fixed in advance
the probability of success, p, is the same on each trial
successive trials are independent of each other
Where should the bootstrap distribution be centered at?
sample statistic
what is the probability of a randomly selected person is male or drives a sports car? P(A or B)
P(A)+P(B)-P(A and B)
60/240+84/240 -39/240 = .25+.35 - .1625
if a confidence internal doesn't contain the null hypothesis, do we reject or fail to reject?
reject the null.
what is the binomial probability function? and explain each variable
P(X=k) = (n/k)p^k(1-p)^n-k
n =trials
p=probability of success
k= probability of exact successes
If a coin is tossed 10 times, what is probability of getting exactly six heads?
P(x=6) = 10C6 * 0.5^6 * 0.5^4 = 210 * 0.015625 * 0.0625 = 0.205078125
If you alpha level is .05 and you get a pvalue of .043, what is our conclusion?
reject the null since P-value is less than alpha
Draw a tree diagram for two coin flips. What is the probability of getting Heads twice?
HH = .5*.5 = .25
Inside our confidence interval
What are the mean and standard deviation for binomial random variable?
mu = n*p
standard deviation = the square root of np(1-p)
60% of people who purchase sports cars are men. If 10 sports car owners are randomly selected, find the probability that exactly 7 are men.
(10C7).6^7(1-.6)^3 = 120 × 0.0279936 × 0.064 = 0.215.
If you collect data where the sample statistics phat1-phat2=4. What would we need to do to the data to create a randomization distribution?
add four to all of phat2 data. a randomization distribution needs to be centered at the null being 0