Math  /  Data & Statistics

QuestionA 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. \begin{tabular}{lllllll} \hline Height (cm) of President & 178 & 176 & 176 & 174 & 191 & 173 \\ \hline Height (cm) of Main Opponent & 162 & 188 & 164 & 168 & 190 & 186 \\ \hline \end{tabular} 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\mu_{d} is the mean value of the differences dd for the population of all pairs of data, where each individual difference dd 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\mathrm{H}_{0}: \mu_{\mathrm{d}} \square \square cm H1:μd\mathrm{H}_{1}: \mu_{\mathrm{d}} \square \square cm (Type integers or decimals. Do not round.)

Studdy Solution
Define the null and alternative hypotheses:
- Null Hypothesis (H0 H_0 ): The mean difference in heights (μd \mu_d ) is equal to 0 cm. - Alternative Hypothesis (H1 H_1 ): The mean difference in heights (μd \mu_d ) is greater than 0 cm.
H0:μd=0cmH_0: \mu_d = 0 \, \text{cm} H1:μd>0cmH_1: \mu_d > 0 \, \text{cm}
The null and alternative hypotheses are defined as above. Proceed with the next steps to calculate the differences and perform the hypothesis test.

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