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   Height (cm) of Main Opponent
179   166
182   173
173   175
191   174
192   180
182   175

a. Use the sample data with a

0.050.05

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,

mu Subscript dμd

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?

Upper H 0H0​:

mu Subscript dμd

▼

not equals≠

equals=

greater than>

less than<

nothing cm

Upper H 1H1​:

mu Subscript dμd

▼

not equals≠

greater than>

less than<

equals=

nothing cm

​(Type integers or decimals. Do not​ round.)

Identify the test statistic.

tequals=nothing

​(Round to two decimal places as​ needed.)

Identify the​ P-value.

​P-valueequals=nothing

​(Round to three decimal places as​ needed.)

What is the conclusion based on the hypothesis​ test?

Since the​ P-value is

▼

less than or equal to

greater than

the significance​ level,

▼

reject

fail to reject

the null hypothesis. There

▼

is

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

nothing

cmless than<mu Subscript dμdless than<nothing

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

▼

only positive numbers,

zero,

only negative numbers,

▼

reject

fail to reject

the null hypothesis.

Enter your answer in each of the answer boxes.

Answer 1