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# Sports and Leisure Let r be the population correlation coefficient between two variables. A…

Sports and Leisure Let r be the population correlation coefficient between two variables. A hypothesis test for a correlation different from zero is based on the sample correlation coefficient, R (the random variable), and involves the t distribution.

A new mountain climber believes that there is a linear relationship between the diameter of a single rope and its dry weight. A random sample of climbing ropes was obtained. The diameter of each was measured (x, in mm) and the weight of each (y, in grams per meter) was also recorded. The data are given in the following table.

a. Find the sample correlation coefficient, and conduct a two-sided hypothesis test with H0: r = 0. Use a significance level of 0.05.

b. Find the estimated regression line, and conduct a test of H0: β1 = 0 versus Ha: b1 ≠ 0. Use a significance level of 0.05.

c. Explain the similarities between the values of the test statistics in parts (a) and (b). Explain why this relationship makes sense.