Question

Consider the following competing hypotheses:

H0: ρxy ≥ 0

HA: ρxy < 0

The sample consists of 34 observations and the sample correlation coefficient is –0.39. Use Table 2.

a. Calculate the value of the test statistic. (Negative value should be indicated by a minus sign. Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.) Test statistic

b. Approximate the p-value. 0.01 < p-value < 0.025 p-value < 0.005 0.05 < p-value < 0.10 0.025 < p-value < 0.05 c. At the 1% significance level, what is the conclusion to the test?

(Do not regect/regect) H0, we (can/cannot) conclude that the population correlation coefficient between x and y is significantly different from zero.

Answer 1

H0: ρxy ≥ 0

HA: ρxy < 0

a) Sample correlation coefficient= -0.39

Sample size =34

Degree of freedom =n-2= 32

test statistic formula is

$=-0.39\sqrt{\frac{34-2}{1-(-0.39)^2}}$

=-2.3959

Test statistic value is -2.40

b) P value for test statistic is =0.0112

0.01 < p-value < 0.025

Do not reject H0, we cannot conclude that the population correlation coefficient between x and y is significantly different from zero.