Exam 3 Flashcards
point estimate
single number that is our “best guess” for a parameter
properties of good estimators (3)
- sampling distribution centered at parameter (unbiased)
- small standard deviation
- relatively efficient (small variance)
interval estimate
interval within which the parameter is believed to fall
2 properties that define interval estimate
margin of error
confidence level
margin of error
measures how accurate the point estimate is likely to be
confidence level
probability of interval containing the parameter
formula for interval for μ, assuming that σ is known
3 common confidence levels with z(𝛼/2)
correct way to describe conclusion with a confidence interval
with –% confidence, we can say that the interval contains the parameter
formula for minimum sample size needed for an interval estimate of μ
E = margin of error
way to get crude σ if not given
σ ≈ range/6
formula for interval for μ, assuming σ is not known
as n ↑, t ….
approaches z (standard normal distr)
point estimate for pop proportion
p hat
formula for p hat, q hat
formula for interval for p
formula for minimum sample size needed for proportion
if p hat is not given on sample size problem…
use p hat = 0.5
chi square characteristics
right skewed
area = 1.00
no negatives
“left” chi value
x^2 (1-𝛼/2)
“right” chi value
x^2 (𝛼/2)
formula for σ interval
for what CI is chi square used?
variance/std dev
chi value 𝛼 gives area to the….
right of the critical value
3 methods of HT
traditional method
p-value method
confidence interval method
hypothesis
statement about a population, usually of the form that a certain parameter takes a particular numerical value or falls in a certain range
null hypothesis states…
that there is no difference between parameter and value
alternative hypothesis states…
that there is a difference between parameter and value
conclusion language if claim is H0
“enough/not enough evidence to reject”
conclusion language if claim is H1
“enough/not enough evidence to support”
type II error
symbol
H0 is not true, but you fail to reject H0
β
type I error
symbol
H0 is true, but you reject it
𝛼
default 𝛼 for HT
0.05
when to use right tail test
H1: parameter > #
when to use left tail test
H1: parameter < #
when to use two tail test
H1: parameter ≠ #
traditional HT method steps
1) hypotheses & claim
2) critical values
3) test statistic
4) decision
5) conclusion
formula to generate z test stat for HT
p-value
area of rejection region(s)
probability of getting an extreme sample statistic in the direction of H1
in the p-value method you presume…
H0 is true
how to find p-value
z table or normalcdf
p-value decision rule
reject H0 if p-val < 𝛼
low p-value increases probability of…
H1 being true
T-test method of HT used when…
σ is unknown
formula to generate t test stat for HT
use for proportion HTs
z-test
formula to generate z test stat for proportion HT
chi-square is used for HT for which parameter?
σ or σ^2
formula to generate chi test stat for variance HT
2 tests used on qualitative variables
goodness of fit
test for independence
GOF used when…
there is one variable
what question does GOF answer?
how well does observed data fit what is expected?
formula to generate chi test stat for GOF and TFI
GOF and TFI use ——- distribution
chi square
DF for GOF
H0 and H1 for GOF
H0: p1 = #, p2 = #, etc
H1: at least one proportion is different
TFI used when…
there are more than one variable in a contingency table
what question does TFI answer?
is there a relationship between the variables?
DF for TFI
H0 and H1 for TFI
H0: no relationship/independent
H1: there is a relationship/dependent
how to find expected values in each cell for TFI
cell notation
