Question

A sample of 6 head widths of seals (in cm) and the corresponding weights of the seals (in kg) were recorded. Given a linear correlation coefficient of 0.948, find the corresponding critical values, assuming a 0.01 significance level. Is there sufficient evidence to conclude that there is a linear correlation?

A. Critical values = ±0.917; there is sufficient evidence to conclude that there is a linear correlation.

B. Critical values = ±0.917; there is not sufficient evidence to conclude that there is a linear correlation.

C. Critical values = ±0.959; there is sufficient evidence to conclude that there is a linear correlation.

D. Critical values = ±0.959; there is not sufficient evidence to conclude that there is a linear correlation.

Answer 1

Solution:

We are given

H₀: There is no any significant linear correlation.

H_a: There is a significant linear correlation.

n = 6,

α = 0.01,

r = 0.948

Critical values = ± 0.917

(by using table for critical values for correlation coefficients)

Value of r is greater than absolute critical value, so we reject the null hypothesis H₀.

Answer:

A. Critical values = ±0.917; there is sufficient evidence to conclude that there is a linear correlation.