A popular theory is that presidential candidates have an advantage if they are t

Question

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 183 186 173 179 195 166 178 188 166 169 181 Height (cm) of Main Opponent 176 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, Ho 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? Type integers or decimals. Do not round.) ldentify the test statistic. (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 opponents. the significance level, | the null hypothesis. There | | sufficient evidence to support the claim that presidents tend to be taller than their Enter your answer in each of the answer boxes.

Explanation / Answer

null Hypothesis:
µd 0

Alternative Hypothesis:
µd = 0

Test Statistic, t: 0.7574
Critical t: 1.822397
P-Value: 0.2336

p value > significance level , failed to reject null hypothesis , there no sufficient evidence to support claim

Degrees of freedom: 9.4898

90% Confidence interval:
-5.624068 < µ1-µ2 < 13.62407

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