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 191 182 179 183 200 174 Height (cm)of Main Opponent 183 185 178 181 184 176 a. Use the sample data with a 0.01significance 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? Identify the test statistic. t= Identify the P-value. P-value = 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 cm<μd< cm. What feature of the confidence interval leads to the same conclusion reached in part (a)? Since the confidence interval contains , __ the null hypothesis.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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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	191	182	179	183	200	174
Height (cm)of Main Opponent	183	185	178	181	184	176

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?

Identify the test statistic.

Identify the P-value.

P-value =

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 ____ cm<μd<____ cm.

What feature of the confidence interval leads to the same conclusion reached in part (a)?

Since the confidence interval contains ______, ______ the null hypothesis.

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