Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
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: _________________