Question Type 8: Performing a hypothesis test for correlation under bivariate normality Exercises

Calculate the sample correlation coefficient $r$ for the data set: (345, 453), (234, 112), (45, 887), (216, 593), (543, 953), (143, 438), (576, 299), (396, 548), (222, 671), (341, 554).

Test at the 5% significance level (two‐tailed) the null hypothesis $H_0:\rho=0$ against $H_1:\rho\neq0$ for the data above.

At the 5% significance level (one‐tailed), test $H_0:\rho=0$ against $H_1:\rho>0$ for the data set.

Test at the 10% significance level (two‐tailed) $H_0:\rho=0$ against $H_1:\rho\neq0$ for the same data.

At the 10% level (one‐tailed), test $H_0:\rho=0$ versus $H_1:\rho>0$ for the same data set.

At the 1% significance level (one‐tailed), test $H_0:\rho=0$ against $H_1:\rho>0$ for the same data.

Test at the 1% significance level (two‐tailed) the null hypothesis $H_0:\rho=0$ against $H_1:\rho\neq0$ for the same data.

At the 5% significance level (one‐tailed), test $H_0:\rho=0$ against $H_1:\rho<0$ for the same data.

Use Fisher's $z$‐transformation to test at the 5% level $H_0:\rho=0.4$ versus $H_1:\rho>0.4$ for the same data.

Use Fisher's $z$‐transformation to test at the 5% level the null hypothesis $H_0:\rho=0.3$ against $H_1:\rho\neq0.3$ for the data above.

At the 1% level, test $H_0:\rho=0.6$ versus $H_1:\rho<0.6$ using Fisher's $z$ for the data.

At the 5% level, test $H_0:\rho=0.5$ against $H_1:\rho\neq0.5$ via Fisher's $z$ for the data.