| from Moore
Sketching xbars for H0, p-value p. 323, 6.25 SSHA 6.26 Spending on housing - - - - - - - - - - - - - - - - - - - Stating null and alternative hypotheses p. 325 6.27, 28, 29, 30 - - - - - - - - - - - - - - - - - - - Calculating p-value (one-sided), relating to Sig. level p. 328, 6.31 and 32 (extending 6.25 and 26) 6.33 restating jargon - - - - - - - - - - - - - - - - - - - Calculating p-value (one or two-sided), using z test statistic, relating to Sig. level p. 333, 6.34 price reduc. on coffee 6.35 crankshafts true? Use your calculator to find the sample mean. 6.36 cola? Use your calculator to find the sample mean. - - - - - - - - - - - - - - - - - - - - - - More p-values p.341, 6.44 CEO pay. Keep a copy of your z test statistic for use in 6.48 next time. p. 343, 6.54 knife edge .05 p. 345, 6.55 and 56 effect of n = = = = = = = = = = = = = = = = *These will be part of Monday's assignment (& on the exam) *p. 342, 6.52 1% vs 5% * 6.53 define stat. signif. p. 341, *6.46, general z statistic, significance,(6.49 will be assigned too.) p. 342 *6.50 patent protection; another z. |
Read,
to discuss |
Optional
(more practice) Stating null and alternative hypotheses
|
>> CI
quiz If you missed
the quiz Wednesday, you may take the quiz, today after class or Monday
before (10 min before, in classroom) or after class---or by arrangement.
>>HW questions?
Cautions on Confidence intervals:(pp. 312-13) Our formula depends on SRS.
Nonresponse or other selection bias can destroy our conclusions.
Outliers, skewness can
mess us up. Nonnormality can mess us up, esp. if sample size is < 15.
These cautions will hold
for Significance Testing also.
Significance
testing
Introduction Day32
Example: H0:
µ =1000 hrs. (Average
lightbulb life.) Design a
competing bulb: Show it's better.
Ha:
µ > 1000 hrs.
Sample of size n = 25.
Population sigma = 150 hrs. Get xbar = 1060 hrs. Are
these bulbs better?
z
= (1060-1000)
÷
(150/5) = 2.
P(Z > 2) = .0228 More than 2% and less than 3%
chance of getting a result this high if we did it again.
"Significant at the alpha =.03 level. Also at the alpha = .05
level"
"Not significant at the alpha = .02 level. Also not significant
at the alpha = .01 level"
Shoebox results: From Last year's
dotplot
White #s
(green box) 2/17 = 11.8% of xbars found are significant. at 10%
Yellow #
(red top box) 13/16 are sig. at 10% If µ is bigger
than
20 by a goodly amount, the test successfully detects this.
(this year?)
2-sided (2-tailed) test:
H0: "Null hypothesis" A
claim or statement about the population we would like to show
is
NOT true.
H0:
µ =1000 hrs. (Average lightbulb life.)
Ha: "Alternative hypothesis"
A claim or statement about the population we are trying to
find
evidence FOR. A value either much bigger than or much
smaller
than the H0 value is evidence against H0 &
for
Ha.
Ha: µ Not = 1000 hrs. (Quality
control
on assembly line--find if it is "off" either way.)
Sample of size n = 25.
Population sigma = 150 hrs. Suppose xbar = 940 hrs. z
= (940-1000)
÷
(150/5) = - 2
P-value: We measure the
probability
of seeing something (again) as extreme as the observed
value
(or more so).
So you need to measure the P-value symmetrically
both directions from the observed value--so the P value is double
what it would be for a one-sided test. P-value
is approximately 5%; more precisely, 2·.0228 =
.0456
Our test is just
barely significant at the .05 level; it is
significant at the .06 level, the .10 level. It's not significant
at the .02 level or "higher".
Meaning of "significance"
(note--"High" significance means small alpha or P-value.)
Question: How do we know that .05 is
"significant?"
(.05
is 1 in 20 chance of seeing the result by "dumb luck" if the null
hypothesis
is true.) Read sec. 6.3, pp. 343-345
>>Significance levels vary by field of
study;
different fields have different "customarily acceptable" levels.
In reality, no
sharp border between "significance" and "not significant"
>>How small a P is "convincing evidence"
against
H0? In practice...
How
plausible is H0? Ha? Strong evidence
needed to reject "conventional wisdom."
How
expensive (mentally, economically) will abandoning H0 be?
>>"Statistically Significant" doesn't
always
mean "Important." (e.g. medicine: "Clinically significant.") Big
enough sample sizes will allow you to distinguish even small
differences.
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