The sample correlation coefficient between x and y is 0.375.It has been found out that the p-value is 0.256 when testing H₀: $\rho$ = 0 against the two-sided alternative H₁: $\rho$ $\neq$ 0.To test H₀: $\rho$ = 0 against the one-sided alternative H₁: $\rho$ 0 at a significant level of 0.193,the p-value will be equal to A) 0.128 B) 0.512 C) 0.744 D) 0.872

Question

The sample correlation coefficient between x and y is 0.375.It has been found out that the p-value is 0.256 when testing H₀: $\rho$ = 0 against the two-sided alternative H₁: $\rho$ $\neq$ 0.To test H₀: $\rho$ = 0 against the one-sided alternative H₁: $\rho$ > 0 at a significant level of 0.193,the p-value will be equal to A) 0.128 B) 0.512 C) 0.744 D) 0.872

Quizplus · Accepted Answer

Since the alternative hypothesis is one-sided, we need to divide the given level of significance (0.193) by 2 in order to find the area of rejection. Therefore, the critical value of the test is z = 1.645 (from the standard normal distribution).

To calculate the p-value for the test, we first need to calculate the test statistic:
t = r * sqrt(n-2) / sqrt(1-r^2) = 0.375 * sqrt(20) / sqrt(1-0.375^2) = 1.458

where r is the sample correlation coefficient and n is the sample size.

Since the alternative hypothesis is one-sided, the p-value will be the area in the upper tail of the t-distribution with 18 degrees of freedom (since we have n-2 = 18 degrees of freedom). Using a t-table or calculator, we find that the p-value is 0.128. Therefore, the answer is A.

The Sample Correlation Coefficient Between X and Y Is 0 ρ\rhoρ

The Sample Correlation Coefficient Between X and Y Is 0 $\rho$