Question

A sample of 10 observations provides the following statistics: ??! = 13, ??! =18, ?????? ??!" = 117.22.

1-Calculate and interpret the sample coefficient ??xy

2-Specify the hypotheses to determine whether the population correlation

coefficient is positive.

3- Calculate the value of the test statistics. Approximate the p-value.

4- At the 5% significance level, what is the conclusion to the test? Explain.

Answer 1

Given s_x = 13, s_y = 18, sxy = 117.22, and n = 10

Answer 1

rxy = s_xy/s_x*s_y = 117.22/(13*18) = 0.5009

Answer 2

H₀:?_xy?0

H_A:?_xy>0

Answer 3

df = n?2 = 10 -2 = 8

The value of the Test statistic, t = r_xy*SQRT[(n-2)/(1-r_xy²)]

Test statistic, t = 0.5009*SQRT[(10-2)/(1-0.5009²)]

Test statistic, t = 1.6369

The p-value is between 0.05 and 0.10 (Obtained using t distribution table screenshot attached)

Answer 4

Since with ? (Level of significance) = 0.05, the p-value > ?, we do not reject H₀. At the 5% significance level, we cannot conclude that the population correlation coefficient between x and y is positive.