A popular theory is that presidential candidates have an advantage if they are taller than their main opponents Listed are

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A popular theory is that presidential candidates have an advantage if they are taller than their main opponents Listed are heights in centimeters of randomly selected presidents along with the heights of their main opponents Complete parts a and b below Height cm of President 179 187 167 182 198 171 Height cm of Main Opponent 168 177 181 177 179 169 a Use the sample data with a 0 05 significance level to test the claim that for the population of heights for presidents and their main opponents the differences have a mean greater than 0 cm In this example is the mean value of the differences d for the population of all pairs of data where each individual difference d is defined as the president s height minus their main opponent s height What are the null and alternative hypotheses for the hypothesis test Ho Pd H Hd cm Type integers or decimals Do not round Identify the test statistic cm t Round to two decimal places as needed Identify the P value P value Round to three decimal places as needed What is the conclusion based on the hypothesis test Since the P value is the significance level the null hypothesis There sufficient evidence to

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