Part 2. Association between Two Variables Measured at Interval/Ratio Level 1) Ma

Question

Part 2. Association between Two Variables Measured at Interval/Ratio Level

1) Mary computed the correlation between two variables. She found that the correlation is moderately strong and positive, r = .38. This association is based on 30 subjects selected at random. Mary wants to know at =0.05 if this correlation is significantly different from 0. Use your 5-steps for hypothesis testing procedure to answer this question.

2)The variables below were collected from a random sample of 10 precincts during the last national election.

A. Graph the association between voter turnout (this is the % of registered voters who voted in the election) and % of the total votes that went to Democratic party using a scattergram (also called a scatterplot).

B. Describe the direction of the association, whether the association appears linear, and identify whether there are any outliers.

C. Political scientists often predict that high voter turnout favors Democratic candidates. Calculate the sample correlation, r, then, using =0.05 and our 5-steps for hypothesis testing, determine whether this sample supports this hypothesis.

Voter Turnout (X)

% of Vote

Democratic (Y)

Voter Turnout (X)

% of Vote

Democratic (Y)

(x - x) (x - x)^2 y-) (y - )^2 (x - x)(y - ) 56 50 55 45 52 56 60 78 89 55 75 85 64 62 45 33 62 25 36 49

Explanation / Answer

(1) n = 30, r = 0.38

From the table of critical values for correlation, for n = 30 and = 0.05, critical r = 0.361

Since 0.38 > 0.361, the correlation is significant

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