Math Problem Statement
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) with the data here. The height (cm) of president is : 183, 179, 168, 189, 189, 170. the height ( cm) of main opponent is : 177,171,173,174,195,183. Part A asks : 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, ųd 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?
Solution
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Math Problem Analysis
Mathematical Concepts
Hypothesis Testing
Paired t-test
Significance Level
Mean Difference
Formulas
Null Hypothesis (H0): μd = 0
Alternative Hypothesis (H1): μd > 0
Test Statistic for Paired t-test: t = (mean difference - hypothesized mean) / (standard deviation of differences / sqrt(n))
Theorems
Central Limit Theorem
T-distribution
Suitable Grade Level
Undergraduate Statistics
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