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. 192 185 174 180 194 177 2 Height (cm) of President Height (cm) of Main Opponent 175 173 167 184 188 179 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, Hd 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?

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
icon
Related questions
Topic Video
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 (em) of President
Height (cm) of Main Opponent 175 173 167 184 188 179
192 185 174 180 194 177 9
a. Use the sample data with a 0.05 significance level to test the cdaim that for the population of heights for presidents and their main opponents, the differences have a mean greater
than O cm.
In this example, Ha 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?
Ho: Ha- 0 om
H1: Ha 0 om
(Type integers or decimals. Do not round.)
Identify the test statistic.
t=O (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
the significance level,
the null hypothesis. There
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 O cm < g <O 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
the null hypothesis.
Transcribed Image Text: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 (em) of President Height (cm) of Main Opponent 175 173 167 184 188 179 192 185 174 180 194 177 9 a. Use the sample data with a 0.05 significance level to test the cdaim that for the population of heights for presidents and their main opponents, the differences have a mean greater than O cm. In this example, Ha 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? Ho: Ha- 0 om H1: Ha 0 om (Type integers or decimals. Do not round.) Identify the test statistic. t=O (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 the significance level, the null hypothesis. There 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 O cm < g <O 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 the null hypothesis.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 4 images

Blurred answer
Knowledge Booster
Hypothesis Tests and Confidence Intervals for Means
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.
Similar questions
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman