Question

3. In class we analyzed data on whether taller US presidential candidate won the election. Analyze the data for 1932-2012 below (note: Mitt Romney is 1 inch taller than Barrack Obama). Frequency 15 taller shorter construct 95% confidence interval for the proportion that taller US presidential candidates won the election based on exact binomial distribution. Show your work.

Do not use normal approximation method. The question is asking for exact binomial distribution method. Ans: 95%CI=(0.51,0.91)

Answer 1

here alpha = 0.05

hence alpha/2 = 0.025

f	cdf
0	9.09495E-13
1	5.54792E-11
2	1.61072E-09
3	2.9605E-08
4	3.86532E-07
5	3.81303E-06
6	2.95117E-05
7	0.000183704
8	0.000935392
9	0.003942142
10	0.013864417
11	0.040925168
12	0.101811857
13	0.214218052
14	0.382827346
15	0.585158497
16	0.774843952
17	0.908739568
18	0.975687375
19	0.996828788
20	1

not that

P(X<= 10) = 0.0138

P(X<= 11) = 0.0409

hence lower limit is l = 10 approx

similary

upper limit is u = 18

(10/20,18/20)

=(0.5,0.9)   approximation in 1 decimal