Question

A sample of 24 observations provides the following statistics: [You may find it useful to reference the t table.]

sx = 19, sy = 16, and sxy = 118.75

a-1. Calculate the sample correlation coefficient rxy. (Round your answer to 4 decimal places.)

a-2. Interpret the sample correlation coefficient rxy.

A. The correlation coefficient indicates a positive linear relationship.
B. The correlation coefficient indicates a negative linear relationship.
C. The correlation coefficient indicates no linear relationship.

b. Specify the hypotheses to determine whether the population correlation coefficient is positive.

A. H0: ρxy = 0; HA: ρxy ≠ 0
B. H0: ρxy ≥ 0; HA: ρxy < 0C.
H0: ρxy ≤ 0; HA: ρxy > 0

c-1. Calculate the value of the test statistic. (Round intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.)

c-2. Find the p-value.

A. 0.01 p-value < 0.025
B. p-value < 0.01
C. p-value 0.10
D. 0.025 p-value < 0.05
E. 0.05 p-value < 0.10

d. At the 1% significance level, what is the conclusion to the test?

Reject H0; we can state the population correlation is positive.
Reject H0; we cannot state the population correlation is positive.
Do not reject H0; we can state the population correlation is positive.
Do not reject H0; we cannot state the population correlation is positive.

Answer 1

a-1. The sample correlation coefficient

a-2. The correlation coefficient indicates a positive linear relationship.

b) H0: ρxy ≤ 0; HA: ρxy > 0

c) The test statistic can be written as

which under H₀ follows a t distribution with n-2 df.

We reject H₀ at the 1% significance level if P-value < 0.01

c-1. The value of the test statistic

c-2) P-value

ans-> D. 0.025 p-value < 0.05

d) Since p-value > 0.01, so we fail to reject H₀ at the 1% significance level.

ans-> Do not reject H0; we cannot state the population correlation is positive.