Task 3 Flashcards
Define statistical inference
draws conclusions about a population or process from sample data
Name 2 types of statistical inference
- confidence intervals
2. tests of significance
What do the statistical inferences report?
both report probabilities that state what would happen if we used the inference method many times
When you use stat. inference, you assume the data came from what kind of sample or experiment?
random
How do you calculate a confidence interval?
C = estimate +or- margin of error
How do you calculate the margin of error?
z* x σ/square root of n
Define confidence interval
for a parameter is an interval computed from sample data bu a method that has probability C of producing an interval containing the true parameter value
How do you find the area on either side of a confidence interval
1-C/2
Name 2 desirable characteristics of a confidence interval
- high confidence 2. small margin of error
Name 3 ways of reducing the margin of error
- use a lower confidence level
- choose a larger n
- reduce standard deviation
What is the formula for the sample size for desired maring of error?
(z x σ)/m²
Define significance test
a formal procedure for comparing observed data with a hypothesis whose truth we want to address
-> results are expressed in terms of a probability
Differentiate between null and alternative hypothesis
Ho: the statement we want to prove wrong
Ha: the statement we want to prove right
Define statistical significance
the chosen boundary for the p-value, if the p-value becomes equal to or smaller than this number than this number, we reject the Ho, siginificant
aka alpha and usually = 0.05
Define critical value
a value z* with a specified area to its right under the standard normal curve, it is the p-value of exactly 5%
Define power
opposite of type 2 error, the probability of correctly rejecting the incorrect Ho
To increase the power (x3)
- increase alpha (bad solution as type 1 error increases)
- increase n (makes estimator more efficient by decreasing standard error)
- bigger effect (however we cannot control this)
I μtrue - μ I
Define a type 1 error
rejecting Ho when it is true (i.e. accepting Ha)
Deine type 2 error
accepting Ho when it is not true (i.e. rejecting Ha)
What is alpha the probability of?
a type 1 error
How do you calculate a type 2 error using power?
1-p(type 2 error)
If your alpha is too high you increase the probability of a type _ error and decrease the probability of a type _ error
1, 2
What happens to the p-value on 2 sided tests?
you halve the p-value
If zobs is greater than z* the z-score therefore falls into ______
the critical area
