Refer to the data set of 20 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 results, does it appear that grader height is an advantage for presidential candidates? Why or why not? **President and Opponent Height Comparison**This table compares the heights of various U.S. Presidents with the heights of their opponents.| President | Height (cm) | Opponent Height (cm) ||--------------|-------------|----------------------|| Wilson | 180 | 182 || Harrison | 173 | 168 || Taylor | 173 | 174 || Eisenhower | 179 | 178 || Pierce | 178 | 196 || Harrison | 168 | 180 || J. Adams | 170 | 189 || Hayes | 173 | 178 || Buchanan | 183 | 175 || Johnson | 192 | 180 || Garfield | 183 | 187 || Jackson | 185 | 171 || Lincoln | 193 | 188 || Hoover | 182 | 180 || Coolidge | 178 | 180 || G. W. Bush | 183 | 185 || Taft | 182 | 178 || G. H. W. Bush| 188 | 173 || Reagan | 185 | 177 || Clinton | 188 | 188 |**Analysis:**This table provides a clear comparison of the physical stature between each President and their opponent during the election. It is interesting to note variations in height and how these might correlate with the public perception of leadership qualities. Several entries show Presidents taller than their opponents, with Lincoln being the tallest at 193 cm, whereas some Presidents, like Pierce, faced opponents much taller than themselves.Height could be a minor factor influencing public perception, though historical and political contexts hold more substantial sway in elections.

Out of the given sample of size, n = 20 the number of presidents whose heights were more than their opponents is = 10 the sample proportion of presidents whose heights were more than their opponents, p^ = 10/20 = 0.5 A 95% confidence interval estimate of the population percentage is p^ ± zα/2×p^(1-p^)/n= 0.5 ± 1.96×0.5×0.5/20= 0.5 ± 0.2= 0.3 to 0.7 i.e., the proportion of presidents whose heights were more than their opponents is around 30% to 70%. Since the confidence interval contains the chance of presidents whose heights were more than their opponents is around 50%. It does not suffice the idea that greater height is an advantage for presidential candidates.