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)ofPresident

191

179

178

175

186

171

Height(cm)ofMainOpponent

180

173

169

180

184

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 mainopponents, the differences have a mean greater than 0 cm.

In thisexample, d is the mean value of the differences d for the population of all pairs ofdata, where each individual difference d is defined as thepresident's height minus their mainopponent's height. What are the null and alternative hypotheses for the hypothesistest?

H0: d

less than

<

not equals

greater than

>

equals

=

nothing

cm

H1: d

equals

=

not equals

greater than

>

less than

<

nothing

cm

(Type integers or decimals. Do notround.)

Identify the test statistic.

t=

nothing

(Round to two decimal places asneeded.)

Identify theP-value.

P-value=

nothing

(Round to three decimal places asneeded.)

What is the conclusion based on the hypothesistest?

Since theP-value is

greater than

less than or equal to

the significancelevel,

fail to reject

reject

the null hypothesis. There

is

is not

sufficient evidence to support the claim that presidents tend to be taller than their opponents.