1. 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

2. 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

3. 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

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

5. Review Slippery Issues
Major Confusion:

6. Review Slippery Issues
Major Confusion:
Population Quantities

7. Review Slippery Issues
Major Confusion:
Population Quantities

8. Review Slippery Issues
Major Confusion:
Population Quantities

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

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

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

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

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

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

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

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

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

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

19. 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

20. Levels of Probability
Simple Events

21. Levels of Probability
Simple Events
Big Rules of Prob

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

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

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

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

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

27. 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

28. 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

29. 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

30. 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

31. Levels of Probability
Distributions (in general)

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

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

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

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

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

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

38. 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

39. 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

40. 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.

41. 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

42. Build Problem Solving Skills
Decisions you need to make

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

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

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

46. 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)

47. Review Decisions Needed
Main Challenge

48. Review Decisions Needed
Main Challenge: Word problems on statistical inference

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

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

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

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

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

54. Review Decisions Needed
Probability model

55. Review Decisions Needed
Probability model:
Proportions

56. Review Decisions Needed
Probability model:
Proportions – Counts

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

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

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

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

61. Review Decisions Needed
Probability model:
Proportions

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

82. 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

83. 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

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

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

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

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

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

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

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

91. 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

92. Review Decisions Needed
3. Inference Type

93. Review Decisions Needed
3. Inference Type:
Confidence Interval

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

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

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

97. Review Decisions Needed
3. Inference Type:
Confidence Interval

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

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

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

101. 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

102. 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…)

103. 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…)

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

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

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

107. 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

108. 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

109. 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…)

110. Review Decisions Needed
Summary of decisions

111. Review Decisions Needed
Summary of decisions
1. Big picture

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

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

114. 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))

115. 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

116. 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)

117. Practice Making Decisions
Print all HW pages

118. Practice Making Decisions
Print all HW pages
Randomly choose page

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

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

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

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

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

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

125. 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?

126. 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

127. And now for something completely different…
Two issues

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

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

130. And now for something completely different…
Professional Statisticians Dislike Excel

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

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

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

134. And now for something completely different…
Professional Statisticians Dislike Excel:
Very poor handling of numerics
Formerly: Unacceptable?!?
Jeff Simonoff Example:
(Problem with Earlier Versions of Excel)

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

136. 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]

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

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

139. 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…

140. 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…”

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

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

143. 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

144. 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

145. 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

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

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

148. 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”…

149. 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…

150. And now for something completely different…
Fun personal story:

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

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

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

154. And now for something completely different…
Fun personal story:
Colin 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

155. And now for something completely different…
Fun personal story:
Colin 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

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

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

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

159. 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

160. 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

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

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

163. 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

164. 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 , every time I noted an organizational inconsistency

165. 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 , every time I noted an organizational inconsistency
Over the semester, I sent around 30 s about all of these

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

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

168. 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

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

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

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

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

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

174. 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)

175. 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

176. 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!

177. Some Examples
Attempt to illustrate how to avoid common mistakes

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

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

180. 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

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

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

183. 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?

184. 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

185. 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!)

186. 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

187. 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.

188. Hypothesis Testing
Suppose observe:

189. Hypothesis Testing
Suppose observe: ,

190. Hypothesis Testing
Suppose observe: ,
based on

191. Hypothesis Testing
Suppose observe: ,
based on
Note

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

193. 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?)

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

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

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

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

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

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

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

201. (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)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

220. 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

221. 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”

222. 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….

223. Hypothesis Testing
E.g. Old text book problem 6.34

224. 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.

225. 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

226. 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….

227. 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”)

228. 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)

229. 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

230. 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?”

231. 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

232. 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

233. 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).

234. 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

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

236. 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

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

238. 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

239. 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

240. 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

241. 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

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

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

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

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

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

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

248. 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

249. 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.

250. 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.

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

252. 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.

253. 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

254. And Now for Something Completely Different
Google Search for:
“And now for something completely different”
Gives more than 100 results….
A perhaps interesting one:

255. 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 And Now for Something Completely Different. P: Dead bugs on windshield. ... stat-or.unc.edu/webspace/postscript/marron/Teaching/stor /Stor ppt - Similar pages