Words matter No one doubts that the words we write or speak are an expression of

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Words matter No one doubts that the words we write or speak are an expression of our inner thoughts and personalities. For example, the use of cognitive words such as "know," "think," "consider," and "always" have been known to indicate high levels of thinking in a person. A curious statistics student would like to test if presidential candidates who win the presidency use more cognitive words than their opponents during presidential debates. To test his hypothesis, the student took a random sample of 10 presidential debates and for each debate recorded a score that reflects the amount of cognitive words used by each of the two candidate, a total of 20 scores, with higher scores indicating more cognitive words. The student is not sure which test to perform, so he would like your help. He has provide R output for both procedures, a paired t-test and independent t-test. R output: Paired t-test data: winner and loser t1.926, df- 9, p-value0.043 alternative hypothesis: true difference in means is greater than 0 Levene's Test for Homogeneity of Variance (center"mean" Df F value Pr(>F) group 1 0.078 0.783 18 Welch Two Sample t-test data: score by debate t2.194, df 17.988, p-value 0.021 alternative hypothesis: true difference in means is greater than 0 Two Sample t-test data: score by debate t 2.194, df- 18, p-value 0.021 alternative hypothesis: true difference in means is greater than 0 Question 10 Subquestions 10.a 2 point(s) The student is not sure which test to perform, so he would like your help Based on how the data were collected, which of the two procedures is appropriate for assessing if presidential candidates who win the presidency (winners) use more cognitive words than their opponents (losers) during presidential debates, on average? Write a short paragraph explaining to the student which of the two procedures is appropriate: paired t test or independent t test

Explanation / Answer

Paired-t tests and independent-samples t tests, both test hypotheses about differences between two means. However, main difference between them is that for independent-samples t test tests the means for the same variable but for two different populations whereas for Paired-t test tests the means for the different variables but for same populations.

For the given problem, the student took random sample of 10 presidential elections and for each debate recorded scores which depends on number of cognitive words used by each of the presidential candidate. So, we are comparing mean scores of 10 samples which are independent as they are obtained from different population (presidential candidate). So independent t test should be used for the given problem.

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