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 180 187 170 178 186 171 Height (cm) of Main Opponent 175 179 164 179 197 181 Question content area bottom Part 1 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, μd 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? H0: μd ▼ less than< equals= greater than> not equals≠ enter your response here cm H1: μd ▼ equals= less than< not equals≠ greater than> enter your response here cm (Type integers or decimals. Do not round.) Part 2 Identify the test statistic. t=enter your response here (Round to two decimal places as needed.) Part 3 Identify the P-value. P-value=enter your response here (Round to three decimal places as needed.) Part 4 What is the conclusion based on the hypothesis test? Since the P-value is ▼ less than or equal to greater than the significance level, ▼ fail to reject reject the null hypothesis. There ▼ is not is sufficient evidence to support the claim that presidents tend to be taller than their opponents. Part 5 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 enter your response here cm<μd

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 180 187 170 178 186 171 Height (cm) of Main Opponent 175 179 164 179 197 181 Question content area bottom Part 1 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, μd 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? H0: μd ▼ less than< equals= greater than> not equals≠ enter your response here cm H1: μd ▼ equals= less than< not equals≠ greater than> enter your response here cm (Type integers or decimals. Do not round.) Part 2 Identify the test statistic. t=enter your response here (Round to two decimal places as needed.) Part 3 Identify the P-value. P-value=enter your response here (Round to three decimal places as needed.) Part 4 What is the conclusion based on the hypothesis test? Since the P-value is ▼ less than or equal to greater than the significance level, ▼ fail to reject reject the null hypothesis. There ▼ is not is sufficient evidence to support the claim that presidents tend to be taller than their opponents. Part 5 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 enter your response here cm<μd

Holt Mcdougal Larson Pre-algebra: Student Edition 2012

1st Edition

ISBN:9780547587776

Author:HOLT MCDOUGAL

Publisher:HOLT MCDOUGAL

Chapter11: Data Analysis And Probability

Section11.4: Collecting Data

Problem 4E

See similar textbooks

Height (cm) of President	180	187	170	178	186	171
Height (cm) of Main Opponent	175	179	164	179	197	181

Question content area bottom

Part 1

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,

μd

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?

H0:

μd

▼

less than<

equals=

greater than>

not equals≠

enter your response here

H1:

μd

▼

equals=

less than<

not equals≠

greater than>

enter your response here

(Type integers or decimals. Do not round.)

Part 2

Identify the test statistic.

t=enter your response here

(Round to two decimal places as needed.)

Part 3

Identify the P-value.

P-value=enter your response here

(Round to three decimal places as needed.)

Part 4

What is the conclusion based on the hypothesis test?

Since the P-value is

▼

less than or equal to

greater than

the significance level,

▼

fail to reject

reject

the null hypothesis. There

▼

is not

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

Part 5

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

enter your response here

cm<μd<enter your response here

cm.

(Round to one decimal place as needed.)