Question

During the last election, a director of a political campaign was interested in whether there was a positive

linear relation between voters’ perceptions that his candidate supported labor unions (Variable X) and

their willingness to vote for his candidate (variable Y). Twenty potential voters were randomly sampled

and asked to indicate on a 10-point rating scale the extent to which they thought that the candidate

supported labor unions, and on another 10-point rating scale their willingness to vote for the candidate

(higher numbers indicate greater perceived support for labor unions and greater willingness to vote for the

candidate). The sample correlation between variables X and Y was .50. Complete the appropriate

hypothesis test, using alpha = .05.

Answer 1

n = 20

r = 0.50

significance level = 0.05

The hypothesis being tested is:

Ho : p = 0

Ha : p > 0

test statistic t = r*sqrt(n-2)/sqrt(1-r^2)

= 0.50*sqrt(20-2)/sqrt(1-(0.50)^2)

t = 2.45

degree of freedom = n - 2= 20 - 2 = 18

t critical value = 1.734

Since 2.45 > 1.734, we can reject the null hypothesis.

Therefore, we have sufficient evidence to reject the claim.

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