Chapter 8 Flashcards
Hypothesis
Claim about the property of the population
Hypothesis test (test of significance)
Procedure testing claim about a property of a population .
p
population proportion
Things to consider
Context, source, and sampling data
Null Hypothesis, Ho
A statement or value of pop. parameter equal to claimed value; no change or effect. Always test the Ho. =
Alternative hypothesis, research hypothesis, H1, HA
A statement or value of pop. parameter differs from null. > (right tailed) ,< (left tailed),≠ (2 tailed)
Test statistic
Sample value used to determine if we accept or reject null hypothesis
Test statistic: Proportion
z=p̂-p/✓pq/n
Test statistic: Mean
z=x̄-μ/σ/✓n or t=-x̄-μ/s/✓n
Test statistic: Standard deviation
x²=(n-1) s²/σ²
Critical region, rejection region
Set of values to reject null hypothesis (area after critical value)
Significance level, α
P that the test stat will fall in critical region when null is true, P of making a mistake of rejecting the null.
P-value definition
P of getting a value in the critical region.
P-value≤α=no go P-value>α=null fly
Type 1 error, α
Mistake of rejecting the null when it’s true
Type 2 error, β
Mistake of failing to reject the null when it’s false
Power (1-β)
P of rejecting a false null. 0.8 is common
P value procedure left tailed
Area to left of test statistic
P value procedure right tailed
Area to right of test stat
P value procedure 2 tailed
2x the area of the tail the test stat is in
Solving: P-value Medthod
Find z for p. Look at area in tail(s) compared to α. Make sure area relates to tails.
P-value≤α=no go P-value>α=null fly
Solving: Traditional Method
Find z of p. Find z of α. Compare z’s. If test stat falls in critical region, reject Ho
Solving: CI
Find CI with E. (Level of confidence:1 tailed:1-2α 2 tailed:1-α)
If CI does not include pop parameter, reject null.
Final statement
There (is or is not) sufficient evidence to (warrant rejection >< or support≠) the claim that (original claim).
8 steps to solve:
Step 1, Symbolic form
Step 2, If step 1 is false then (opposite step 1)
Step 3 If there is no equal sign, use I as H1.
Step 4 Select a significance level).05 or 0.01.
Step 5 Determine what formula and chart to use
Step 6 Find test stat and (P-value or critical region)
Step 7 Fail to or reject the null
Step 8 Restate with “significant evidence”
Requirements Normal Distribution Approximation
- Simple random sample
- binomial requirements
- np≥5 nq≥5
How to find μ and σ
μ=np σ=✓npq
Exact method
Requirement check, P value of null. (=x or more, p̂>p=2x x or more, p̂<p=2x x or less) Use
Requirements mean: σ known
Simple random, σ is known, simple random or n>30
Finding P-value: σ unknown
They must tell you the area. look at #’s in row of df. Get the range of area in tail based off rows actual area is in-between.