Download here

The Chicago High School for the Arts
AP Statistics
Unit 4: Inference
Name: ________________________________
Date: _________________
Unit 4 Exam Review – Important Formulas, Terminology & Calculator Commands
Chapter 8: Confidence Intervals
Interpretation of Confidence Level –
Interpretation of Confidence Interval –
Confidence Interval for Proportions
Conditions
Confidence Interval
Formula
Choosing the
Sample Size
Confidence Interval
on the Calculator
Confidence Intervals for Means
The Chicago High School for the Arts
AP Statistics
Unit 4: Inference
Name: ________________________________
Date: _________________
Chapter 9: Significance Tests
Type I error –
Type II error –
Power –
Significance Test for Proportions
Hypotheses
Conditions
Test Statistic
P-value
Significance Test
Conclusion
Significance Test on the
Calculator
Significance Tests for Means
The Chicago High School for the Arts
AP Statistics
Unit 4: Inference
Name: ________________________________
Date: _________________
Unit 4 Exam Review – Important Formulas, Terminology & Calculator Commands
Chapter 8: Confidence Intervals
Interpretation of Confidence Level – “___% of all possible samples of a given size from this population
will result in an interval that captures the unknown parameter.”
Interpretation of Confidence Interval – “We are ___% confident that the interval from ___ to ___
captures the actual value of the population parameter.”
Conditions
Confidence Interval
Formula
Confidence Interval for Proportions
Random
Independent – check 10% condition:
10𝑛 ≤ 𝑁
Normal – check sample size conditions:
𝑛𝑝 ≥ 10
𝑛(1 − 𝑝) ≥ 10
Confidence Intervals for Means
Random
Independent – check 10% condition:
10𝑛 ≤ 𝑁
Normal – check sample size conditions:
𝑛 ≥ 30
If 𝑛 < 30, then you can assume the
Normal distribution as long as 𝑛 ≥ 15
& the sample is approximately
symmetric.
𝑠𝑡𝑎𝑡𝑖𝑠𝑡𝑖𝑐 ± (𝑐𝑟𝑖𝑡𝑖𝑐𝑎𝑙 𝑣𝑎𝑙𝑢𝑒)
∙ (𝑠𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑠𝑡𝑎𝑡𝑖𝑠𝑡𝑖𝑐)
𝑠𝑡𝑎𝑡𝑖𝑠𝑡𝑖𝑐 ± (𝑐𝑟𝑖𝑡𝑖𝑐𝑎𝑙 𝑣𝑎𝑙𝑢𝑒)
∙ (𝑠𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑠𝑡𝑎𝑡𝑖𝑠𝑡𝑖𝑐)
𝑥̅ ± 𝑡 ∗
𝑝(1 − 𝑝)
𝑝̂ ± 𝑧 ∗ √
𝑛
𝑠𝑥̅
√𝑛
If 𝜎 is unknown
OR
𝑥̅ ± 𝑧 ∗
𝜎
√𝑛
If 𝜎 is known
Choosing the
Sample Size
𝑧
𝑝(1 − 𝑝)
≤ 𝑚𝑎𝑟𝑔𝑖𝑛 𝑜𝑓 𝑒𝑟𝑟𝑜𝑟
𝑛
∗√
𝑧∗
𝜎
√𝑛
≤ 𝑚𝑎𝑟𝑔𝑖𝑛 𝑜𝑓 𝑒𝑟𝑟𝑜𝑟
Solve for n.
Solve for n.
Confidence Interval
on the Calculator
To find 𝑧 ∗ : 2nd Vars invNorm(lower tail
probability)
To find 𝑡 ∗ : use the Table with degrees
of freedom = n – 1
To find CI: Stat Tests 1-PropZInt
x: # of successes, n: sample size, Clevel: confidence level
Calculate
To find CI: Stat Tests TInterval Stats
𝑥̅ : sample mean, 𝑠𝑥 : sample standard
deviation, C-level: confidence level
Calculate
The Chicago High School for the Arts
AP Statistics
Unit 4: Inference
Name: ________________________________
Date: _________________
Chapter 9: Significance Tests
Type I error – Reject 𝐻0 when 𝐻0 is really true (Type I error = ).
Type II error – Fail to reject 𝐻0 when 𝐻0 is really false (Type II error = ).
Power – Correctly reject 𝐻0 when 𝐻0 is really false (Power = 1 – Type I error = 1 – ).
Hypotheses
Conditions
Significance Test for Proportions
𝐻0 : 𝑝 = 𝑝0
𝐻𝑎 : 𝑝 > 𝑝0 (one-sided test)
𝐻𝑎 : 𝑝 < 𝑝0 (one-sided test)
𝐻𝑎 : 𝑝 ≠ 𝑝0 (two-sided test)
Significance Tests for Means
𝐻0 : 𝜇 = ____
𝐻𝑎 : 𝜇 > ____ (one-sided test)
𝐻𝑎 : 𝜇 < ____ (one-sided test)
𝐻𝑎 : 𝜇 ≠ ____ (two-sided test)
Random
Independent – check 10% condition:
10𝑛 ≤ 𝑁
Normal – check sample size
conditions:
𝑛𝑝0 ≥ 10
𝑛(1 − 𝑝0 ) ≥ 10
Random
Independent – check 10% condition:
10𝑛 ≤ 𝑁
Normal – check sample size
conditions:
𝑛 ≥ 30
If 𝑛 < 30, then you can assume the
Normal distribution as long as 𝑛 ≥
15 & the sample is approximately
symmetric.
Test Statistic
𝑧=
𝑝̂ − 𝑝0
√𝑝0 (1 − 𝑝0 )
𝑛
Tells you how many standard
deviations 𝑝̂ is from the null
hypothesis parameter 𝑝0 .
P-value
Area under curve =
p-value
Total area under
curve = p-value
𝑡=
𝑥̅ − 𝜇
𝑠𝑥
√𝑛
Tells you how many standard
deviations 𝑥̅ is from the null
hypothesis parameter.
Same as for proportions, but with
appropriate hypotheses and test
statistic t.
Significance Test
Conclusion
If p-value is less than the prior stated
level of significance, 𝛼, reject 𝐻0 . If
p-value is greater than or equal to
the prior stated level of significance,
𝛼, fail to reject 𝐻0 . NEVER accept 𝐻0 .
If p-value is less than the prior stated
level of significance, 𝛼, reject 𝐻0 . If
p-value is greater than or equal to
the prior stated level of significance,
𝛼, fail to reject 𝐻0 . NEVER accept 𝐻0 .
Significance Test on the
Calculator
To find the p-value: 2nd Vars
normalcdf(lower bound =z-score,
upper bound=100)
To find the p-value: 2nd Vars
tcdf(lower bound =t-score, upper
bound=100)
To run the whole test: Stat Tests 1PropZTest
To run the whole test: Stat Tests TTest
The Chicago High School for the Arts
AP Statistics
Unit 4: Inference
Name: ________________________________
Date: _________________