Final Examination Thursday, April 30, 4:00 – 7:00 Location: here, Hanes 120 Suggested Study Strategy: Rework HW Out of Class Review Session? No, personal Q-A much better use of time Thus, instead offer extended Office Hours

Final Examination Thursday, April 30, 4:00 – 7:00 Location: here, Hanes 120 Suggested Study Strategy: Rework HW Out of Class Review Session? No, personal Q-A much better use of time Thus, instead offer extended Office Hours Bring with you, to exam: Single (8.5" x 11") sheet of formulas Front & Back OK

Final Examination Extended Office Hours Monday, April 27, 8:00 – 11:00 Tuesday, April 28, 12:00 – 2:30 Wednesday, April 29, 1:00 – 5:00 Thursday, April 30, 8:00 – 1:00

Last Time Unmatched 2 Sample Hypothesis Testing Linear Regression Fit lines to scatterplots Least squares fit Excel functions Diagnostic: Residual Plot Prediction

Review Slippery Issues Major Confusion:

Review Slippery Issues Major Confusion: Population Quantities

Review Slippery Issues Major Confusion: Population Quantities

Review Slippery Issues Major Confusion: Population Quantities

Review Slippery Issues Major Confusion: Population Quantities vs. Sample Quantities

Review Slippery Issues Major Confusion: Population Quantities vs. Sample Quantities

Review Slippery Issues Major Confusion: Population Quantities vs. Sample Quantities

Review Slippery Issues Major Confusion: Population Quantities vs. Sample Quantities Called Parameters

Review Slippery Issues Major Confusion: Population Quantities vs. Sample Quantities Called Parameters Called Statistics

Review Slippery Issues Major Confusion: Population Quantities vs. Sample Quantities Unknown

Review Slippery Issues Major Confusion: Population Quantities vs. Sample Quantities Unknown, Goal is to estimate

Review Slippery Issues Major Confusion: Population Quantities vs. Sample Quantities Unknown, Goal is to estimate, Use to fix ideas

Review Slippery Issues Major Confusion: Population Quantities vs. Sample Quantities Unknown, Goal is to estimate, Use to fix ideas Get from data

Review Slippery Issues Major Confusion: Population Quantities vs. Sample Quantities Unknown, Goal is to estimate, Use to fix ideas Get from data, Called “estimates”

Review Slippery Issues Major Confusion: Population Quantities vs. Sample Quantities Unknown, Goal is to estimate, Use to fix ideas Get from data, Called “estimates”, Know these

Levels of Probability Simple Events

Levels of Probability Simple Events Big Rules of Prob

Levels of Probability Simple Events Big Rules of Prob (Not, And, Or)

Levels of Probability Simple Events Big Rules of Prob (Not, And, Or) Bayes Rule

Levels of Probability Simple Events Distributions Big Rules of Prob (Not, And, Or) Bayes Rule Distributions

Levels of Probability Simple Events Distributions (in general) Big Rules of Prob (Not, And, Or) Bayes Rule Distributions (in general)

Levels of Probability Simple Events Distributions (in general) Big Rules of Prob (Not, And, Or) Bayes Rule Distributions (in general) Defined by Tables

Levels of Probability Simple Events Distributions (in general) Big Rules of Prob (Not, And, Or) Bayes Rule Distributions (in general) Defined by Tables Summary of discrete probs

Levels of Probability Simple Events Distributions (in general) Big Rules of Prob (Not, And, Or) Bayes Rule Distributions (in general) Defined by Tables Summary of discrete probs Get probs by summing

Levels of Probability Simple Events Distributions (in general) Big Rules of Prob (Not, And, Or) Bayes Rule Distributions (in general) Defined by Tables Summary of discrete probs Get probs by summing Uniform

Levels of Probability Simple Events Distributions (in general) Big Rules of Prob (Not, And, Or) Bayes Rule Distributions (in general) Defined by Tables Summary of discrete probs Get probs by summing Uniform Get probs by finding areas

Levels of Probability Distributions (in general)

Levels of Probability Distributions (in general) Named (& Useful) Distributions

Levels of Probability Distributions (in general) Named (& Useful) Distributions Binomial

Levels of Probability Distributions (in general) Named (& Useful) Distributions Binomial Discrete distribution of Counts

Levels of Probability Distributions (in general) Named (& Useful) Distributions Binomial Discrete distribution of Counts Compute with BINOMDIST & Normal Approx.

Levels of Probability Distributions (in general) Named (& Useful) Distributions Binomial Discrete distribution of Counts Compute with BINOMDIST & Normal Approx. Normal

Levels of Probability Distributions (in general) Named (& Useful) Distributions Binomial Discrete distribution of Counts Compute with BINOMDIST & Normal Approx. Normal Continuous distribution of Averages

Levels of Probability Distributions (in general) Named (& Useful) Distributions Binomial Discrete distribution of Counts Compute with BINOMDIST & Normal Approx. Normal Continuous distribution of Averages Compute with NORMDIST & NORMINV

Levels of Probability Distributions (in general) Named (& Useful) Distributions Binomial Discrete distribution of Counts Compute with BINOMDIST & Normal Approx. Normal Continuous distribution of Averages Compute with NORMDIST & NORMINV T

Levels of Probability Distributions (in general) Named (& Useful) Distributions Binomial Discrete distribution of Counts Compute with BINOMDIST & Normal Approx. Normal Continuous distribution of Averages Compute with NORMDIST & NORMINV T Similar to Normal, for estimated s.d.

Levels of Probability Distributions (in general) Named (& Useful) Distributions Binomial Discrete distribution of Counts Compute with BINOMDIST & Normal Approx. Normal Continuous distribution of Averages Compute with NORMDIST & NORMINV T Similar to Normal, for estimated s.d. Compute with TDIST & TINV

Build Problem Solving Skills Decisions you need to make

Build Problem Solving Skills Decisions you need to make While taking Final Exam

Build Problem Solving Skills Decisions you need to make While taking Final Exam When faced with a word problem

Build Problem Solving Skills Decisions you need to make While taking Final Exam When faced with a word problem Key to deciding on approach

Build Problem Solving Skills Decisions you need to make While taking Final Exam When faced with a word problem Key to deciding on approach (e.g. knowing which formula to use)

Review Decisions Needed Main Challenge

Review Decisions Needed Main Challenge: Word problems on statistical inference

Review Decisions Needed Main Challenge: Word problems on statistical inference Choices to keep in mind

Review Decisions Needed Main Challenge: Word problems on statistical inference Choices to keep in mind: Big picture

Review Decisions Needed Main Challenge: Word problems on statistical inference Choices to keep in mind: Big picture: Single Sample

Review Decisions Needed Main Challenge: Word problems on statistical inference Choices to keep in mind: Big picture: Single Sample Two Samples

Review Decisions Needed Main Challenge: Word problems on statistical inference Choices to keep in mind: Big picture: Single Sample Two Samples Regression

Review Decisions Needed Probability model

Review Decisions Needed Probability model: Proportions

Review Decisions Needed Probability model: Proportions – Counts

Review Decisions Needed Probability model: Proportions – Counts (p based)

Review Decisions Needed Probability model: Proportions – Counts (p based) Normal Means

Review Decisions Needed Probability model: Proportions – Counts (p based) Normal Means – Measurements

Review Decisions Needed Probability model: Proportions – Counts (p based) Normal Means – Measurements (μ based)

Review Decisions Needed Probability model: Proportions

Review Decisions Needed Probability model: Proportions – Counts (p based)

Review Decisions Needed Probability model: Proportions – Counts (p based) Best Guess

Review Decisions Needed Probability model: Proportions – Counts (p based) Best Guess Conservative

Review Decisions Needed Probability model: Proportions – Counts (p based) Best Guess Conservative BINOMDIST

Review Decisions Needed Probability model: Proportions – Counts (p based) Best Guess Conservative BINOMDIST Normal Approx to Binomial

Review Decisions Needed Probability model: Proportions – Counts (p based) Best Guess Conservative BINOMDIST Normal Approx to Binomial (used usually for Hypo tests, etc.)

Review Decisions Needed Probability model: b. Normal Means (mu based)

Review Decisions Needed Probability model: b. Normal Means (mu based) Sigma known

Review Decisions Needed Probability model: b. Normal Means (mu based) Sigma known – NORMDIST & NORMINV

Review Decisions Needed Probability model: b. Normal Means (mu based) Sigma known – NORMDIST & NORMINV Sigma unknown

Review Decisions Needed Probability model: b. Normal Means (mu based) Sigma known – NORMDIST & NORMINV Sigma unknown – TDIST & TINV

Review Decisions Needed Probability model: (Keeping Excel functions straight) Cutoff → Prob

Review Decisions Needed Probability model: (Keeping Excel functions straight) Cutoff → Prob

Review Decisions Needed Probability model: (Keeping Excel functions straight) Cutoff → Prob

Review Decisions Needed Probability model: (Keeping Excel functions straight) Cutoff → Prob

Review Decisions Needed Probability model: (Keeping Excel functions straight) Cutoff → Prob Prob → Cutoff

Review Decisions Needed Probability model: (Keeping Excel functions straight) Cutoff → Prob Prob → Cutoff Counts, Prop’ns

Review Decisions Needed Probability model: (Keeping Excel functions straight) Cutoff → Prob Prob → Cutoff Counts, Prop’ns BINOMDIST ???

Review Decisions Needed Probability model: (Keeping Excel functions straight) Cutoff → Prob Prob → Cutoff Counts, Prop’ns BINOMDIST ??? Meas. σ known

Review Decisions Needed Probability model: (Keeping Excel functions straight) Cutoff → Prob Prob → Cutoff Counts, Prop’ns BINOMDIST ??? Meas. σ known NORMDIST NORMINV

Review Decisions Needed Probability model: (Keeping Excel functions straight) Cutoff → Prob Prob → Cutoff Counts, Prop’ns BINOMDIST ??? Meas. σ known NORMDIST NORMINV Meas. σ unkno’n

Review Decisions Needed Probability model: (Keeping Excel functions straight) Cutoff → Prob Prob → Cutoff Counts, Prop’ns BINOMDIST ??? Meas. σ known NORMDIST NORMINV Meas. σ unkno’n TDIST TINV

Review Decisions Needed Probability model: (Keeping Excel functions straight)

Review Decisions Needed Probability model: (Keeping Excel functions straight) Recall horrible Excel Organizations

Review Decisions Needed Probability model: (Keeping Excel functions straight) Recall horrible Excel Organizations Different functions work differently

Review Decisions Needed Probability model: (Keeping Excel functions straight) Recall horrible Excel Organizations Different functions work differently Indicate these on formula sheet…

Review Decisions Needed Probability model: (Keeping Excel functions straight) What about ??? (in above table)

Review Decisions Needed Probability model: (Keeping Excel functions straight) What about ???: There is no BINOMINV

Review Decisions Needed Probability model: (Keeping Excel functions straight) What about ???: There is no BINOMINV Since tricky to invert discrete prob’s

Review Decisions Needed Probability model: (Keeping Excel functions straight) What about ???: There is no BINOMINV Since tricky to invert discrete prob’s Have to use Normal Approx to Binomial

Review Decisions Needed 3. Inference Type

Review Decisions Needed 3. Inference Type: Confidence Interval

Review Decisions Needed 3. Inference Type: Confidence Interval Choice of Sample Size

Review Decisions Needed 3. Inference Type: Confidence Interval Choice of Sample Size Hypothesis Testing

Review Decisions Needed 3. Inference Type: Confidence Interval Choice of Sample Size Hypothesis Testing (each has its set of formulas…)

Review Decisions Needed 3. Inference Type: Confidence Interval

Review Decisions Needed 3. Inference Type: Confidence Interval Binomial type: Best guess, NORMINV

Review Decisions Needed 3. Inference Type: Confidence Interval Binomial type: Best guess, NORMINV Binomial type: Conservative, NORMINV

Review Decisions Needed 3. Inference Type: Confidence Interval Binomial type: Best guess, NORMINV Binomial type: Conservative, NORMINV Normal, σ known: NORMINV or CONFIDENCE

Review Decisions Needed 3. Inference Type: Confidence Interval Binomial type: Best guess, NORMINV Binomial type: Conservative, NORMINV Normal, σ known: NORMINV or CONFIDENCE Normal, σ unknown: TINV

Review Decisions Needed 3. Inference Type: Confidence Interval Binomial type: Best guess, NORMINV Binomial type: Conservative, NORMINV Normal, σ known: NORMINV or CONFIDENCE Normal, σ unknown: TINV (each has its set of formulas…)

Review Decisions Needed 3. Inference Type: Choice of Sample Size Binomial type: Best guess, NORMINV Binomial type: Conservative, NORMINV Normal, σ known: NORMINV Normal, σ unknown: TINV (each has its set of formulas…)

Review Decisions Needed 3. Inference Type: Hypothesis Testing – P-values Binomial type: NORMDIST (or BINOMDIST)

Review Decisions Needed 3. Inference Type: Hypothesis Testing – P-values Binomial type: NORMDIST (or BINOMDIST) Normal, σ known: NORMDIST

Review Decisions Needed 3. Inference Type: Hypothesis Testing – P-values Binomial type: NORMDIST (or BINOMDIST) Normal, σ known: NORMDIST Normal, σ unknown: TDIST

Review Decisions Needed 3. Inference Type: Hypothesis Testing – P-values Binomial type: NORMDIST (or BINOMDIST) Normal, σ known: NORMDIST Normal, σ unknown: TDIST Variation, σ known: Z-stat

Review Decisions Needed 3. Inference Type: Hypothesis Testing – P-values Binomial type: NORMDIST (or BINOMDIST) Normal, σ known: NORMDIST Normal, σ unknown: TDIST Variation, σ known: Z-stat Variation, σ unknown: t-stat

Review Decisions Needed 3. Inference Type: Hypothesis Testing – P-values Binomial type: NORMDIST (or BINOMDIST) Normal, σ known: NORMDIST Normal, σ unknown: TDIST Variation, σ known: Z-stat Variation, σ unknown: t-stat (each has its set of formulas…)

Review Decisions Needed Summary of decisions

Review Decisions Needed Summary of decisions 1. Big picture

Review Decisions Needed Summary of decisions 1. Big picture: (Single - Two Samples – 2 Way Tab’s – Reg’n)

Review Decisions Needed Summary of decisions 1. Big picture: (Single - Two Samples – 2 Way Tab’s – Reg’n) 2. Probability model

Review Decisions Needed Summary of decisions 1. Big picture: (Single - Two Samples – 2 Way Tab’s – Reg’n) 2. Probability model: (Prop’ns (Counts) - Normal (Meas’ts))

Review Decisions Needed Summary of decisions 1. Big picture: (Single - Two Samples – 2 Way Tab’s – Reg’n) 2. Probability model: (Prop’ns (Counts) - Normal (Meas’ts)) 3. Inference Type

Review Decisions Needed Summary of decisions 1. Big picture: (Single - Two Samples – 2 Way Tab’s – Reg’n) 2. Probability model: (Prop’ns (Counts) - Normal (Meas’ts)) 3. Inference Type: (Conf. Int. - Sample Size – Hypo Testing)

Practice Making Decisions Print all HW pages

Practice Making Decisions Print all HW pages Randomly choose page

Practice Making Decisions Print all HW pages Randomly choose page Randomly choose problem

Practice Making Decisions Print all HW pages Randomly choose page Randomly choose problem Work that out

Practice Making Decisions Print all HW pages Randomly choose page Randomly choose problem Work that out (make decisions…)

Practice Making Decisions Print all HW pages Randomly choose page Randomly choose problem Work that out (make decisions…) Mark it off

Practice Making Decisions Print all HW pages Randomly choose page Randomly choose problem Work that out (make decisions…) Mark it off Return & repeat

Practice Making Decisions Print all HW pages Randomly choose page Randomly choose problem Work that out (make decisions…) Mark it off Return & repeat

Practice Making Decisions Print all HW pages Randomly choose page Randomly choose problem Work that out (make decisions…) Mark it off Return & repeat Finish all correctly?

Practice Making Decisions Print all HW pages Randomly choose page Randomly choose problem Work that out (make decisions…) Mark it off Return & repeat Finish all correctly? An easy A in this course

And now for something completely different… Two issues

And now for something completely different… Two issues: What do professional statisticians think about EXCEL?

And now for something completely different… Two issues: What do professional statisticians think about EXCEL? Why are the EXCEL functions so poorly organized?

And now for something completely different… Professional Statisticians Dislike Excel

And now for something completely different… Professional Statisticians Dislike Excel: Very poor handling of numerics

And now for something completely different… Professional Statisticians Dislike Excel: Very poor handling of numerics Formerly: Unacceptable?!?

And now for something completely different… Professional Statisticians Dislike Excel: Very poor handling of numerics Formerly: Unacceptable?!? Jeff Simonoff Example: http://www.stern.nyu.edu/~jsimonof/classes/1305/pdf/excelreg.pdf

And now for something completely different… Professional Statisticians Dislike Excel: Very poor handling of numerics Formerly: Unacceptable?!? Jeff Simonoff Example: http://www.stern.nyu.edu/~jsimonof/classes/1305/pdf/excelreg.pdf (Problem with Earlier Versions of Excel)

And now for something completely different… Old Problem 1: Excel didn’t keep enough significant digits (relative to other software)

And now for something completely different… Old Problem 1: Excel didn’t keep enough significant digits (relative to other software) [single precision vs. double precision]

And now for something completely different… Problem 2: Excel doesn’t warn when troubles are encountered…

And now for something completely different… Problem 2: Excel doesn’t warn when troubles are encountered… All software has its limitation

And now for something completely different… Problem 2: Excel doesn’t warn when troubles are encountered… All software has its limitation But it is easy to provide warnings…

And now for something completely different… Problem 2: Excel doesn’t warn when troubles are encountered… All software has its limitation But it is easy to provide warnings… “Competent software does this…”

And now for something completely different… Why are the EXCEL functions so poorly organized?

And now for something completely different… Why are the EXCEL functions so poorly organized? E.g. NORMDIST uses left areas

And now for something completely different… Why are the EXCEL functions so poorly organized? E.g. NORMDIST uses left areas TDIST uses right or 2-sided areas

And now for something completely different… Why are the EXCEL functions so poorly organized? E.g. NORMDIST uses left areas TDIST uses right or 2-sided areas E.g. NORMINV uses left areas

And now for something completely different… Why are the EXCEL functions so poorly organized? E.g. NORMDIST uses left areas TDIST uses right or 2-sided areas E.g. NORMINV uses left areas TINV uses 2-sided areas

And now for something completely different… Why are the EXCEL functions so poorly organized?

And now for something completely different… Why are the EXCEL functions so poorly organized? Looks like programmer was handed a statistics text

And now for something completely different… Why are the EXCEL functions so poorly organized? Looks like programmer was handed a statistics text, and told “turn these into functions”…

And now for something completely different… Why are the EXCEL functions so poorly organized? Looks like programmer was handed a statistics text, and told “turn these into functions”… Problem: organization was good for table look ups, but looks clunky now…

And now for something completely different… Fun personal story:

And now for something completely different… Fun personal story: Colin Bell @ Microsoft heard about “complaints from statisticians on EXCEL”

And now for something completely different… Fun personal story: Colin Bell @ Microsoft heard about “complaints from statisticians on EXCEL” Decided to “try to fix these”

And now for something completely different… Fun personal story: Colin Bell @ Microsoft heard about “complaints from statisticians on EXCEL” Decided to “try to fix these” Contacted Jeff Simonoff about numerics

And now for something completely different… Fun personal story: Colin Bell @ Microsoft heard about “complaints from statisticians on EXCEL” Decided to “try to fix these” Contacted Jeff Simonoff about numerics Asked Jeff to work with him

And now for something completely different… Fun personal story: Colin Bell @ Microsoft heard about “complaints from statisticians on EXCEL” Decided to “try to fix these” Contacted Jeff Simonoff about numerics Asked Jeff to work with him Jeff refused, doesn’t like or use EXCEL

And now for something completely different… Fun personal story: Jeff told Colin about me

And now for something completely different… Fun personal story: Jeff told Colin about me Colin asked me

And now for something completely different… Fun personal story: Jeff told Colin about me Colin asked me I agreed about numerical problems

And now for something completely different… Fun personal story: Jeff told Colin about me Colin asked me I agreed about numerical problems, but said I had bigger objections about organization

And now for something completely different… Fun personal story: Jeff told Colin about me Colin asked me I agreed about numerical problems, but said I had bigger objections about organization Colin asked me to write these up

And now for something completely different… Fun personal story: I said I was too busy, but…

And now for something completely different… Fun personal story: I said I was too busy, but… I would teach (similar course) soon

And now for something completely different… Fun personal story: I said I was too busy, but… I would teach (similar course) soon. I offered to send an email

And now for something completely different… Fun personal story: I said I was too busy, but… I would teach (similar course) soon. I offered to send an email, every time I noted an organizational inconsistency

And now for something completely different… Fun personal story: I said I was too busy, but… I would teach (similar course) soon. I offered to send an email, every time I noted an organizational inconsistency Over the semester, I sent around 30 emails about all of these

And now for something completely different… Fun personal story: Colin agreed with each of the points made

And now for something completely different… Fun personal story: Colin agreed with each of the points made Colin approached the statistical people at Microsoft

And now for something completely different… Fun personal story: Colin agreed with each of the points made Colin approached the statistical people at Microsoft They agreed that organization could have been done better

And now for something completely different… Fun personal story: But for “backwards compatibility” reasons, refused to change anything

And now for something completely different… Fun personal story: But for “backwards compatibility” reasons, refused to change anything (even when Office 2007 came out…)

And now for something completely different… Fun personal story: But for “backwards compatibility” reasons, refused to change anything Colin apologetically archived all my emails…

And now for something completely different… How much should we worry:

And now for something completely different… How much should we worry: Organization is a pain, but you can live with it

And now for something completely different… How much should we worry: Organization is a pain, but you can live with it (OK to complain when you feel like it)

And now for something completely different… How much should we worry: Organization is a pain, but you can live with it (OK to complain when you feel like it) Usually (except for weird rounding) numerical issues don’t arise

And now for something completely different… How much should we worry: Organization is a pain, but you can live with it (OK to complain when you feel like it) Usually (except for weird rounding) numerical issues don’t arise, but need to be aware of potential!

Some Examples Attempt to illustrate how to avoid common mistakes

Some Examples Attempt to illustrate how to avoid common mistakes Guiding Principle:

Some Examples Attempt to illustrate how to avoid common mistakes Guiding Principle: (& useful color scheme)

Population Quantities Recall Main Framework Need to keep straight: Population Quantities vs. Sample Quantities Unknown, Goal is to estimate, Use to fix ideas Get from data, Called “estimates”, Know these

Hypothesis Testing E.g. A fast food chain currently brings in profits of $20,000 per store, per day

Hypothesis Testing E.g. A fast food chain currently brings in profits of $20,000 per store, per day. A new menu is proposed.

Hypothesis Testing E.g. A fast food chain currently brings in profits of $20,000 per store, per day. A new menu is proposed. Would it be more profitable?

Hypothesis Testing E.g. A fast food chain currently brings in profits of $20,000 per store, per day. A new menu is proposed. Would it be more profitable? Test: Have 10 stores

Hypothesis Testing E.g. A fast food chain currently brings in profits of $20,000 per store, per day. A new menu is proposed. Would it be more profitable? Test: Have 10 stores (randomly selected!)

Hypothesis Testing E.g. A fast food chain currently brings in profits of $20,000 per store, per day. A new menu is proposed. Would it be more profitable? Test: Have 10 stores (randomly selected!) try the new menu

Hypothesis Testing E.g. A fast food chain currently brings in profits of $20,000 per store, per day. A new menu is proposed. Would it be more profitable? Test: Have 10 stores (randomly selected!) try the new menu, let = average of their daily profits.

Hypothesis Testing Suppose observe:

Hypothesis Testing Suppose observe: ,

Hypothesis Testing Suppose observe: , based on

Hypothesis Testing Suppose observe: , based on Note

Hypothesis Testing Suppose observe: , based on Note , but is this conclusive?

Hypothesis Testing Suppose observe: , based on Note , but is this conclusive? or could this be due to natural sampling variation? (i.e. do we risk losing money from new menu?)

Hypothesis Testing E.g. Fast Food Menus: Test

Hypothesis Testing E.g. Fast Food Menus: Test

Hypothesis Testing E.g. Fast Food Menus: Test Using

Hypothesis Testing E.g. Fast Food Menus: Test Using

Hypothesis Testing E.g. Fast Food Menus: Test Using P-value = P{what saw or m.c.| H0 & HA bd’ry}

Hypothesis Testing E.g. Fast Food Menus: Test Using P-value = P{what saw or m.c.| H0 & HA bd’ry}

Hypothesis Testing E.g. Fast Food Menus: Test Using P-value = P{what saw or m.c.| H0 & HA bd’ry}

(guides where to put $21k & $20k) Hypothesis Testing E.g. Fast Food Menus: Test Using P-value = P{what saw or m.c.| H0 & HA bd’ry} (guides where to put $21k & $20k)

Hypothesis Testing P-value = P{what saw or or m.c.| H0 & HA bd’ry}

Hypothesis Testing P-value = P{what saw or or m.c.| H0 & HA bd’ry}

Hypothesis Testing P-value = P{what saw or or m.c.| H0 & HA bd’ry}

Hypothesis Testing P-value = P{what saw or or m.c.| H0 & HA bd’ry}

Hypothesis Testing P-value = P{what saw or or m.c.| H0 & HA bd’ry}

Hypothesis Testing P-value = P{what saw or or m.c.| H0 & HA bd’ry}

Hypothesis Testing P-value = P{what saw or or m.c.| H0 & HA bd’ry}

Hypothesis Testing P-value = P{what saw or or m.c.| H0 & HA bd’ry}

Hypothesis Testing P-value = P{what saw or or m.c.| H0 & HA bd’ry}

Consider Variations Look carefully at how problems can be twiddled, to get opposite answer

Hypothesis Testing CAUTION: Read problem carefully to distinguish between: One-sided Hypotheses

Hypothesis Testing CAUTION: Read problem carefully to distinguish between: One-sided Hypotheses - like:

Hypothesis Testing CAUTION: Read problem carefully to distinguish between: One-sided Hypotheses - like: Two-sided Hypotheses

Hypothesis Testing CAUTION: Read problem carefully to distinguish between: One-sided Hypotheses - like: Two-sided Hypotheses - like:

Hypothesis Testing Hints: Use 1-sided when see words like

Hypothesis Testing Hints: Use 1-sided when see words like: Smaller Greater In excess of

Hypothesis Testing Hints: Use 1-sided when see words like: Smaller Greater In excess of Use 2-sided when see words like:

Hypothesis Testing Hints: Use 1-sided when see words like: Smaller Greater In excess of Use 2-sided when see words like: Equal Different

Hypothesis Testing Hints: Use 1-sided when see words like: Smaller Greater In excess of Use 2-sided when see words like: Equal Different Always write down H0 and HA

Hypothesis Testing Hints: Use 1-sided when see words like: Smaller Greater In excess of Use 2-sided when see words like: Equal Different Always write down H0 and HA Since then easy to label “more conclusive”

Hypothesis Testing Hints: Use 1-sided when see words like: Smaller Greater In excess of Use 2-sided when see words like: Equal Different Always write down H0 and HA Since then easy to label “more conclusive” And get partial credit….

Hypothesis Testing E.g. Old text book problem 6.34

Hypothesis Testing E.g. Old text book problem 6.34: In each of the following situations, a significance test for a population mean, is called for.

Hypothesis Testing E.g. Old text book problem 6.34: In each of the following situations, a significance test for a population mean, is called for. State the null hypothesis, H0

Hypothesis Testing E.g. Old text book problem 6.34: In each of the following situations, a significance test for a population mean, is called for. State the null hypothesis, H0 and the alternative hypothesis, HA in each case….

Hypothesis Testing E.g. 6.34a An experiment is designed to measure the effect of a high soy diet on bone density of rats. Let = average bone density of high soy rats = average bone density of ordinary rats (since no question of “bigger” or “smaller”)

Variation E.g. 6.34a An experiment is designed to see if a high soy diet increases bone density of rats. Let = average bone density of high soy rats = average bone density of ordinary rats (since “bigger” is goal)

Hypothesis Testing E.g. 6.34b Student newspaper changed its format. In a random sample of readers, ask opinions on scale of -2 = “new format much worse”, -1 = “new format somewhat worse”, 0 = “about same”, +1 = “new a somewhat better”, +2 = “new much better”. Let = average opinion score

Hypothesis Testing E.g. 6.34b (cont.) No reason to choose one over other, so do two sided. Note: Use one sided if question is of form: “is the new format better?”

Hypothesis Testing E.g. 6.34c The examinations in a large history class are scaled after grading so that the mean score is 75. A teaching assistant thinks that his students have a higher average score than the class as a whole. His students can be considered as a sample from the population of all students he might teach, so he compares their score with 75. = average score for all students of this TA

Variation E.g. 6.34c The examinations in a large history class are scaled after grading so that the mean score is 75. A teaching assistant thinks that his students have a different average score from the class as a whole. His students can be considered as a sample from the population of all students he might teach, so he compares their score with 75. = average score for all students of this TA

Hypothesis Testing E.g. Textbook problem 6.36 Translate each of the following research questions into appropriate and Be sure to identify the parameters in each hypothesis (generally useful, so already did this above).

Hypothesis Testing E.g. 6.36a A researcher randomly divides 6-th graders into 2 groups for PE Class, and teached volleyball skills to both. She encourages Group A, but acts cool towards Group B. She hopes that encouragement will result in a higher mean test for group A. Let = mean test score for Group A = mean test score for Group B

Hypothesis Testing E.g. 6.36a Recall: Set up point to be proven as HA

Variation E.g. 6.36a A researcher randomly divides 6-th graders into 2 groups for PE Class, and teached volleyball skills to both. She encourages Group A, but acts cool towards Group B. She wonders whether encouragement will result in a different mean test for group A. Let = mean test score for Group A = mean test score for Group B

Variation E.g. 6.36a Recall: Set up point to be proven as HA

Hypothesis Testing E.g. 6.36b Researcher believes there is a positive correlation between GPA and esteem for students. To test this, she gathers GPA and esteem score data at a university. Let = correlation between GPS & esteem

Variation E.g. 6.36b Researcher investigates the potential correlation between GPA and esteem for students. To test this, she gathers GPA and esteem score data at a university. Let = correlation between GPS & esteem

Hypothesis Testing E.g. 6.36c A sociologist asks a sample of students which subject they like best. She suspects a higher percentage of females, than males, will name English. Let: = prop’n of Females preferring English = prop’n of Males preferring English

Variation E.g. 6.36c A sociologist asks a sample of students which subject they like best. Is there a difference between the percentage of females & males, that name English. Let: = prop’n of Females preferring English = prop’n of Males preferring English

And Now for Something Completely Different Etymology of: “And now for something completely different”

And Now for Something Completely Different Etymology of: “And now for something completely different” Anybody heard of this before? (really 2 questions…)

And Now for Something Completely Different Etymology of: “And now for something completely different” Anybody heard of this before? (really 2 questions…)

And Now for Something Completely Different Etymology of: “And now for something completely different” Anybody heard of this before? (really 2 questions…)

And Now for Something Completely Different What is “etymology”?

And Now for Something Completely Different What is “etymology”? Google responses to: define: etymology

And Now for Something Completely Different What is “etymology”? Google responses to: define: etymology The history of words; the study of the history of words. csmp.ucop.edu/crlp/resources/glossary.html

And Now for Something Completely Different What is “etymology”? Google responses to: define: etymology The history of words; the study of the history of words. csmp.ucop.edu/crlp/resources/glossary.html The history of a word shown by tracing its development from another language. www.animalinfo.org/glosse.htm

And Now for Something Completely Different What is “etymology”? Etymology is derived from the Greek word e/)tymon(etymon) meaning "a sense" and logo/j(logos) meaning "word." Etymology is the study of the original meaning and development of a word tracing its meaning back as far as possible. www.two-age.org/glossary.htm

And Now for Something Completely Different Google response to: define: and now for something completely different

And Now for Something Completely Different Google response to: define: and now for something completely different And Now For Something Completely Different is a film spinoff from the television comedy series Monty Python's Flying Circus.

And Now for Something Completely Different Google response to: define: and now for something completely different And Now For Something Completely Different is a film spinoff from the television comedy series Monty Python's Flying Circus. The title originated as a catchphrase in the TV show. Many Python fans feel that it excellently describes the nonsensical, non sequitur feel of the program. en.wikipedia.org/wiki/And_Now_For_Something_Completely_Different

And Now for Something Completely Different Google Search for: “And now for something completely different” Gives more than 100 results…. A perhaps interesting one: http://www.mwscomp.com/mpfc/mpfc.html

And Now for Something Completely Different Google Search for: “Stor 155 and now for something completely different” Gives: [PPT] Slide 1 File Format: Microsoft Powerpoint - View as HTML http://stat-or.unc.edu/webspace/postscript/marron/Teaching/stor155-2007/ ... And Now for Something Completely Different. P: Dead bugs on windshield. ... stat-or.unc.edu/webspace/postscript/marron/Teaching/stor155-2007/Stor155-07-01-30.ppt - Similar pages