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Test of Correlation Coefficient

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1. The following hypotheses are given
H0: rho = 0
H1: rho > 0
A random sample of 12 paired observations indicated a correlation of .32. Can we conclude that the correlation in the population is greater than zero? Use the .05 significance level.

2. The Pennsylvania Refining Company is studying the relationship between the pump price of gasoline and the number of gallons sold. For a sample of 20 stations last Tuesday, the correlation was 0.78. At the .01 significance level, is the correlation in the population greater than zero?
H0: rho = 0
H1: rho > 0.

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The solution provides a test of correlation coefficient.

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