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 nontrivial 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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