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 189 178 181 186 203 167 9 Height (cm) of Main Opponent 165 187 168 175 182 176 Identify the test statistic. t= 1.45 (Round to two decimal places as needed.) Identify the P-value. P-value = 0.104 (Round to three decimal places as needed.) What is the conclusion based on the hypothesis test? Since the P-value is greater than the significance level, fail to reject the null hypothesis. There is not sufficient evidence to support the claim that presidents tend to be taller than their opponents. b. Construct the confidence interval that could be used for the hypothesis test described in part (a). What feature of the confidence interval leads to the same conclusion reached in part (a)? The confidence interval is cm < Ha < cm. (Round to one decimal place as needed.) What feature of the confidence interval leads to the same conclusion reached in part (a)? Since the confidence interval contains the null hypothesis.

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