Stat 31, Section 1, Last Time • Hypothesis Tests – H - , H 0 or H + version of testing – P-values – small for strong evidence – 1-sided (strong evidence for “>” or “<“) – 2-sided (strong evidence for “different”) • Cutoffs – Yes – no (P-val < 0.05, or not?) – Gray level (interpret level…)
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Stat 31, Section 1, Last Time Hypothesis Tests –H -, H 0 or H + version of testing –P-values – small for strong evidence –1-sided (strong evidence for.
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Stat 31, Section 1, Last Time
• Hypothesis Tests
– H-, H0 or H+ version of testing
– P-values – small for strong evidence
– 1-sided (strong evidence for “>” or “<“)
– 2-sided (strong evidence for “different”)
• Cutoffs
– Yes – no (P-val < 0.05, or not?)
– Gray level (interpret level…)
Hypothesis Testing, III
CAUTION: Read problem carefully to distinguish between:
One-sided Hypotheses - like:
Two-sided Hypotheses - like:
:.:0 AHvsH
:.:0 AHvsH
Hypothesis TestingHints:• 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. Text book problem 6.32:
In each of the following situations, a
significance test for a population mean,
mu is called for. State the null
hypothesis, H0 and the alternative
hypothesis, HA in each case….
Hypothesis TestingE.g. 6.32aExperiments on learning in animals
sometimes measure how long it takes a mouse to find its way through mazes. The mean time is 18 seconds for one particular maze. A researcher thinks that a loud noise will cause the nice to complete the maze faster. She measures how long each of 10 mice takes with a noise as stimulus.
= time to finish with loud noise.18:0 H 18: AH
Hypothesis TestingE.g. 6.32bThe examinations in a large history class are
scaled after grading so that the mean score is 50. 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 50.
= average score for all students of this TA50:0 H 50: AH
Hypothesis TestingE.g. 6.32cThe Census Bureau reports that households
spend an average of 31% of their total spending on housing. A homebuilders association in Cleveland wonders if the national finding applies in their area. They interview a sample of 40 households in the Cleveland metropolitan area to learn what percent of their spending goes toward housing.
= avg. % for housing in Cleveland %31:0 H %31: AH
Hypothesis Testing
E.g. Textbook problem 6.34
Translate each of the following research
questions into appropriate and0H AH
Hypothesis TestingE.g. 6.34aCensus Bureau data shows that the mean
household income in the area served by a shopping mall is $62,500 per year. A market research firm questions shoppers at the mall to find out whether the mean household income of mall shoppers is higher that that of the general population.
= average income of mall shoppers 500,62$:0 H
500,62$: AH
Hypothesis TestingE.g. 6.34bLast year, your company’s service
technicians took an average of 2.6 hours to respond to trouble calls from business customers who had purchased service contracts. Do this year’s data show a different average response size?
= average response time 6.2:0 H6.2: AH
Hypothesis Testing
HW on setting up hypotheses:
6.31, 6.33
Hypothesis Testing
Connection between Confidence Intervals
and Hypothesis Tests:
Reject at Level 0.05 P-value < 0.05
dist’n
Area < 0.05
0.95 margin of error
mX
mXmX , CIinnot 95.0
X
Hypothesis Testing & CIs
Reject at Level 0.05
Notes:
1. This is why EXCEL’s CONFIDENCE function uses = 1 – coverage prob.
2. If only care about 2-sided hypos, then could work only with CIs
(and not learn about hypo. tests)
CIinnot 95.0
Hypothesis Testing & CIs
HW: 6.63, 6.64
(a. [59.99,63.59] b. No, 61.3 inside c. No, 63 inside)
Hypothesis Testing
The three traps of Hypothesis Testing
(and how to avoid them…)
Trap 1: Statistically Significant is different
from Really Significant
(don’t confuse them)
Hypothesis Testing Traps
Trap 1: Statistically Significant is different
from Really Significant
E.g. To test a painful diet program, 10,000
people were put on it. Their average
weight loss was 1.7 lbs, with s = 73.
Assess “significance” by hypothesis testing.
Hypothesis Testing Traps
Trap 1: Statistically Significant is different
from Really Significant
See Class Example 23: Trap 1https://www.unc.edu/~marron/UNCstat31-2005/Stat31Eg23.xls