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发帖数: 479 | 1 Scenario A: A Monte Carlo experiment was conducted to compare the widths of
confidence intervals (CIs) produced from two different methods. Briefly,
1000 data sets were randomly generated. To each of the data sets, the two
methods were applied to obtain CIs for the parameter of interest. The widths
below are from 10 of the 1000 data sets. Relevant summary statistics for
all 1000 are provided.
Data Set 1 2 3 4 5 6 7 8 9 … 1000 Mean
SD
B method 1.05 0.77 0.61 0.65 0.73 0.63 0.55 0.50
0.50 … 0.52 0.631 0.124
W method 1.01 0.74 0.62 0.63 0.74 0.61 0.56 0.53
0.50 … 0.52 0.627 0.119
Difference 0.05 0.03 -0.01 0.03 -0.02 0.02 -0.01 -0.
03 0.00 … 0.00 0.004 0.022
A1) What are the research and null hypotheses here? Be sure to define any
symbols you use.
A2) What is the (approximate) p-value for this test?
A3) Use a 95% CI to conduct the test at the .05 significance level.
A4) What assumptions, if any, have you made for parts A2 and/or A3?
Scenario B: From Table 1 of Villanti et al. (2012) AJPH 102:1310-1312.
Villanti et al. examine switching from Menthol Non-menthol cigarettes in a
group of 16-18 year olds (among others) followed from 2003 – 2005.
(count) Didn’t switch Switched Row Totals
Menthol at baseline 87 29 116
Non-menthol at baseline 156 21 177
Column Totals 243 50 293
B1) Calculate the proportion of subjects who switched from smoking menthol
cigarettes at baseline, along with an approximate 95% CI for the true
proportion.
B2) Calculate the proportion of subjects who switched from smoking non-
menthol cigarettes at baseline (no CI needed).
B3) Do the proportions of those who switched differ between those who
initially smoked menthol cigarettes and those who initially smoked non-
menthol cigarettes?
B4) What assumptions, if any, have you made for B1 and B2 of this set? What
additional assumptions, if any, have you made for the last question of this
set? |
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