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 186 183 183 186 193 164 Height (cm) of Main Opponent 180 171 181 172 188 174 a. Use the sample data with a 0.01 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, d 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. t(Round to two decimal places as needed.) ldentify 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 presidents tend to be taller than their opponents | the significance leve | the null hypothesis. There | sufficient evidence to support the claim that

Explanation / Answer

The statistical softwre output for this problem is:

Paired T hypothesis test:
D = 1 - 2 : Mean of the difference between Height of President and Height of Main Opponent
H0 : D = 0
HA : D > 0
Hypothesis test results:

99% confidence interval results:

Hence,

a) Hypotheses:

H0 : D = 0
H1 : D > 0

t = 1.39

p - Value = 0.112

Greater; Do not; is not

b) Confidence interval:

-9.2 < D < 18.9

both positive and negative values (0); Do not reject

Difference Mean Std. Err. DF T-Stat P-value Height of President - Height of Main Opponent 4.8333333 3.4872785 5 1.3859901 0.1122

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