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Hand in (All D&V)Nothing new. I'm making this problem optional. Not required, ever. MCS-353-71 (adapted): Political candidates To get their names on the ballot of a local election, political candidates often must obtain petitions bearing the signatures of a minimum number of registered voters. In Pinellas County, Florida, a certain political candidate obtained petitions with 18,200 signatures (St. Petersburg Times, Apr. 7, 1992). To verify that the names on the petitions were signed by actual registered voters, election officials randomly sampled 100 of the names and checked each for authenticity. Only two were invalid signatures. a) Is 98 out of 100 verified signatures sufficient to believe that more than 17,000 of the total 18,200 signatures are valid? b) Repeat part (a) if only 16,000 valid signatures are required. Based on Statistics, McClave and Sincich, pg. 353 c) Construct a 95% CI for the proportion of valid signatures. Turn the endpoints of the CI into numbers of valid signatures by multiplying by 18,200. Exam 3 material ends here Postpone the rest:- - - - - - - - - - - A. Use the T-table to decide these questions: a) Ho: p = .3 vs. HA: p>.3. z from p-hat is 2.12. Is it significant at the .01 level? .05? .10? b) Ho: p = .3 vs. HA: p not = .3. z from p-hat is 2.12. Is it significant at the .01 level? .05? .10? c) Ho: p = .3 vs. HA: p>.3. z from p-hat is 3.16. Is it significant at the .01 level? .05? .10? p. 387, #11 (use p.397--CI's & Tests) |
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More about :
Especially if we must make a decision to Reject Ho
(or retain it)---
Set "benchmark" or "cutoff" level "alpha"
"significance level": (p. 393-4)
If P-value is less
than alpha, we say the test is "significant at level alpha"
(Seeing the result (again) would be rarer than alpha, if the null hypothesis
is true)
Table T (A-53) bottom row is z-values.
What if you don't have the Z-table but only
have the T-table (Table p. A-53)?
What if you have a demanded level of significance,
alpha?
"Critical value" --the z* corresponding to your alpha (p.394-5
)
T-Table:
a limited list of probabilities across the top row:
= Right tail values for the bell curve distribution. (and
double that for equal-tails)
The
value in the bottom (infinity or z*) row under the probability is the corresponding
standard normal value.
"z*
is the upper p critical value of the standard normal distribution."
Do this: Find your z from
the data. Make a sketch of the normal curve and mark z on it. Mark
the direction(s) of Ha.
(If your z is in the direction
of Ha , continue. Otherwise the results are hopelessly
not significant: you can quit.)
Find the two z*'s in Table T (p.
A-53) that bracket your z
(ignore minus sign).
Find the corresponding p's.
e.g. z =1.83
Two tail p
.10 .05 .02
One tail p
... .05 .025
.01 ...
infinity(z*)
1.645 \/ 1.960 2.326
z = 1.83
Notice as the z's increase, the amounts in the tail(s) decrease.
Test is significant at the bigger bracketing
probability; not sig. at the smaller.
One sided: P-value
is less than .05 and greater than .025
Significant at the .05 level,not
at the .025 level
Two sided: P-value
is less than .10 and greater than .05
Significant at the .10 level,not
at the .05 level
If you have a specific demanded significance
level, compare it with these levels.
Give P-values if you can! (more information)
Confidence Intervals and Hypothesis Tests: (p. 397)
Suppose you're interested in Ho: p = .3 vs.
HA: p not = .3 ( two-sided alternative). If your
95% CI for p DOES NOT include the po value (.3) , then you can
Reject Ho at the .05 level (.05 = 1.00 -.95). This is
approximate, because we use different calculations for the standard deviations,
but good enough if the CI is not close to the po.
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