Refer to the accompanying data set of 20 randomly selected presidents. 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 thepopulation percentage. Based on the result, does it appear that greater height is an advantage for presidential candidates? Why or why not?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.%

It is required to construct the 95% confidence interval for the percentage of presidents taller than their opponents, and decide whether a greater height appears to be an advantage for presidential candidates.Denote p as the true population proportion of presidents taller than their opponents.The 20 randomly selected presidents indicate a sample size of .The heights of the presidents and their respective opponents, along with whether or not the presidents were taller than their opponents, are given in the table below. Note that the value 1 indicates that the president was taller than their opponent, whereas the value 0 indicates that the opponent was taller. Counting the total of the last column “Height > Height Opp?”, that is, counting the number of 1s in this column would give the number of cases in which the president was taller than the opponents, say x.PresidentHeightHeight OppHeight > Height Opp?[1=“Yes”, 0=“No”]Johnson1921801F. Roosevelt1881821Hayes1731780G.W. Bush1831850Harrison1731681Jackson1851711Taylor1731740Buchanon1831751Tafe1821781J Kennedy1831821Van Buren1681800Carter1771830Coolidge1781800Lincoln1931881Harding1831781Cleveland1801800Wilson1801820Hoover1821801Polk1731850G.H.W. Bush1881731Total––Clearly, .Denote p̂ as the sample proportion of presidents taller than their opponents.The sample proportion here is:Thus, the sample proportion of presidents who were taller than their opponents, p̂ is 0.6.It is required to find the 95% confidence interval for the population proportion.The confidence level is, .As a result:This implies that, .The confidence interval for one proportion uses the standard normal distribution, and is two-tailed, requiring two critical values. The positive critical value of the standard normal distribution at the 95% confidence level or 0.05 significance level is zα/2, such that, so that .In this case, or .The Excel formula is:Thus, , so that the critical value is, .Therefore, the 95% confidence interval is calculated below:Thus, the 95% confidence interval for the proportion is (0.331963765, 0.768036235).Multiply the lower and upper bounds of the confidence interval to express them as percentages:.Thus, the 95% confidence interval of the percentage of presidents taller than their opponents is, .If greater height is not an advantage for presidential candidates, then historically, presidents would be randomly taller or shorter than their opponents. In that case, in about 50% of the cases, the presidents would be taller than their opponents, whereas in the remaining 50% of the cases, the presidents would be shorter than their opponents. Any confidence interval containing the value 50% would indicate 50% as a plausible value of the population percentage of presidents taller than their opponents. If, on the other hand, the both the lower and upper limits of the confidence interval are greater than 50% then it would imply that, historically, greater height might have been an advantage for presidential candidates, as more than 50% of the presidents have been taller than their opponents.Here, the confidence interval is from 33.2% to 76.8%, which contains the value 50%. implying that 50% is a feasible true value of the population proportion, so that it does not appear greater height has had any advantage for presidential candidates.Since you have not provided the options for the blanks, we are unable to match exactly with the options. However, we have filled the blanks logically, which would help you identify the exact correct options.The 95% confidence interval estimate of the percentage of presidents taller than their opponents is, .“If greater height was an advantage, then taller candidates should have won more than 50% of the elections. In this case, greater height does not seem to be an advantage for presidential candidates because the confidence interval contains the value 50%.”