Thursday, May 30, 2019

Creating Confidence Intervals for Polling Results



This post calculates confidence intervals for the proportion of Republicans and the proportion of Democrats who support fixing the ACA.   I use Excel to make the calculation and introduce the TINV function.


Question:    199 Democrats and 79 Republicans were asked whether they supported fixing the ACA.   The responses, undecided, against and support are presented in the table below.  Use this data to create a 95 percent confidence interval for the percent of Democrat and Republican respondents who support fixing the ACA.


Fixing The ACA  (# Respondents)
Undecided
82
14
Opposed
45
52
Support
72
13
Total
199
79
Fixing the ACA (% Respondents)
Democrats
Republicans
Undecided
41.2%
17.7%
Opposed
22.6%
65.8%
Support
36.2%
16.5%
Total
100.0%
100.0%



Analysis:

Below is the calculation of the confidence intervals for the proportion of Democrats and the proportion of Republicans who support fixing the ACA.



Calculation of Confidence Intervals for Proportion of
 Respondents who Want to Fix the ACA
Democrats
Republicans
p
0.362
0.165
SE
0.034
0.042
tinv
1.972
1.991
LB
0.295
0.082
UB
0.429
0.248

Some policy comments:


A non-trivial percent of Republicans want to fix, not repeal, the ACA.

A lot of Democrats are now undecided about the ACA. 

It is possible that in five years Democrats will be all in on single payer and Republicans will come around to supporting the ACA.

Some technical comments

Note the due to the smaller sample size the confidence interval for Republicans is much larger than the confidence interval for Democrats.

The t value used to construct the confidence interval was obtained from the t.inv function.  I used TINV(0.05,sample size minus 1).






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