Test #3 Concepts (Ch. 5, 6, 7, 8, 9)
Binomial Distribution
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The 4 assumptions of binomial
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2 possible outcomes
fixed # of trials
constant probability for success
each is trial is independent
You need to be able to identify a binomial
by recognizing these characteristics.
Probabilities using binomial cdf (calculator exercises) [Ch. 5.2&5.3]
Normal Approximation to Binomial [Ch. 6.4]
o Continuity Correction
o Mean & Std. Deviation for approximation
o Finding Probabilities using ~N(np, √npq)
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Sampling Distribution of the Binomial Distribution [Ch. 7.3]
o Point Estimate for population proportion (p ≈ by p-hat)
o Mean & Standard Deviation (Different than 6.4 since linear f(n) of x)
o Continuity Correction (Different than 6.4 since 0.5/n)
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Confidence Intervals for True Population Proportion (1 Sample) [Ch. 8.3]
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Using sample data
Knowing how to find the Critical Value (calculator – inverse normal)
Finding E by formula & using to compute interval
Using the calculator to find the interval
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Confidence Intervals for Difference in Pop. Proportions (2 Sample) [Ch. 8.4]
o Using sample data
o Knowing how to find the Critical Value (calculator – inverse normal)
o Finding E by formula & using to compute interval
o Using the calculator to find the interval
o Inferences based upon the confidence intervals
 Recall: Positive, Negative or Both are points of reference
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Hypothesis Testing for Binomially Distributed RV (1 Sample) [Ch. 9.1/9.2]
o Pinpoint that a RV is binomially distributed
 Recall: 1) More numbers are given than for means 2) See success/failure
situation
o Create null and alternative hypotheses for binomially distributed RV
o Know how to use your calculator to test the hypothesis (STATTESTS1PropZTest)
 List: Test Stat, P-Value & State Conclusion based on info given by calculator
Normal Distribution
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Sample Mean & Standard Deviation Using Data
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Probabilities Under Normal Distribution (1 observation) [Ch. 6.3]
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Probabilities of Average (Sample of size n) [Ch. 7.2]
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Central Limit Theorem
Confidence Intervals
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Estimating the Population Mean when σ is known [Ch. 8.1]
 Using sample data or sample statistics
Y. Butterworth
Test #3 Concepts – Math 10 F10
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 Knowing how to find the Critical Value (calculator – inverse normal)
 Finding E by formula & using to compute interval
 Using the calculator to find the interval
 Inferences based upon the confidence intervals
Estimating the Population Mean when σ is unknown [Ch. 8.2]
 Using sample data or sample statistics
 Knowing how to find the Critical Value (calculator – inverse t)
 Finding E by formula & using to compute interval
 Using the calculator to find the interval
 Inferences based upon the confidence intervals
Estimating the Difference of Population Means [Ch. 8.4]
When σ is known
 Using sample data or sample statistics
 Knowing how to find the Critical Value (calculator – inverse normal)
 Finding E by formula & using to compute interval
 Using the calculator to find the interval
 Inferences based upon the confidence intervals
When σ is unknown
 Using sample data or sample statistics
 Knowing how to find the Critical Value (calculator – inverse t)
 Finding E by formula & using to compute interval
 Using the calculator to find the interval
 Inferences based upon the confidence intervals
Hypothesis Testing [Ch. 9]
General Knowledge [Ch. 9.1]
 Hypotheses Setup
 H0 contains equality
 HA or 1 is research & determines rejection region
 Critical Value – Based on α and rejection region
 Test Statistics (see additional handout)
 Stating a Conclusion Correctly
 Three Types of Tests (use Test Stat & Critical Value from hand or Calculator)
 Traditional Method
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The method most prevalently taught in class
 P-Value Method
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Probability of our test stat is < α for a one tail rejects
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Probability of our test stat x 2 < α for two tail rejects
 Confidence Interval Method
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Right now knowledge used is from 8.4
 Above null rejects right tail
Put another way – null isn’t in
 Below null rejects left tail
 Above or below rejects 2 tail the interval it rejects
One Sample with σ known [Ch. 9.1]
 Know how to set test up & conduct
One Sample with σ unknown [Ch. 9.2]
 Know how to set test up & conduct with calculator only
Y. Butterworth
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Test #3 Concepts – Math 10 F10
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