Question

Refer to the data set of

2020

randomly selected presidents given below. Treat the data as a sample and find the proportion of presidents who were taller than their opponents. Use that result to construct a​ 95% confidence interval estimate of the population percentage. Based on the​ result, does it appear that greater height is an advantage for presidential​ candidates? Why or why​ not?

LOADING...

Click the icon to view the table of heights.

Construct a​ 95% confidence interval estimate of the percentage of presidents who were taller than their opponents.

nothing​%less than<pless than<nothing​%

​(Round to one decimal place as​ needed.)

        More

Enter your answer in the edit fields and then click Check Answer.

1 part remaining

Clear All

Check Answer

President and Opponent Height

PRESIDENT	HEIGHT	HEIGHT OPP
TrumanTruman	175175	173173
McKinleyMcKinley	170170	178178
J. KennedyJ. Kennedy	183183	182182
HarrisonHarrison	168168	180180
HayesHayes	173173	178178
HooverHoover	182182	180180
ReaganReagan	185185	177177
NixonNixon	182182	180180
CarterCarter	177177	183183
J. AdamsJ. Adams	170170	189189
PiercePierce	178178	196196
F. RooseveltF. Roosevelt	188188	182182
JacksonJackson	185185	171171
CoolidgeCoolidge	178178	180180
GarfieldGarfield	183183	187187
JeffersonJefferson	189189	170170
LincolnLincoln	193193	188188
EisenhowerEisenhower	179179	178178
G. H. W. BushG. H. W. Bush	188188	173173
Van BurenVan Buren	168168	180180

Answer 1

N = 20

NUMBER OF PRESIDENCTS WHOSE HEIGHTS ARE GREATER = 11

............

Level of Significance,   α =    0.05          
Number of Items of Interest,   x =   11          
Sample Size,   n =    20          
                  
Sample Proportion ,    p̂ = x/n =    0.5500          
z -value =   Zα/2 =    1.960   [excel formula =NORMSINV(α/2)]      
                  
Standard Error ,    SE = √[p̂(1-p̂)/n] =    0.111243          
margin of error , E = Z*SE =    1.960   *   0.11124   =   0.2180
                  
95%   Confidence Interval is              
Interval Lower Limit = p̂ - E =    0.55000   -   0.21803   =   0.332
Interval Upper Limit = p̂ + E =   0.55000   +   0.21803   =   0.768
                  
95%   confidence interval is (   0.3320   < p <    0.7680   )

0.5 LIE IN THE INTERVAL, SO

THERE IS NOT ENOUGH EVIDENCE THAT greater height is an advantage for presidential​ candidates
..........

THANKS