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.
Using a significance level of 0.01, with 6 pairs of data, the corresponding critical values for a linear correlation coefficient are +/-0.917. Since the calculated correlation coefficient is 0.948, which is larger than the critical value, there is sufficient evidence to conclude that there is a linear correlation. Therefore, the answer is A) Critical values=+-0.917; there is sufficient evidence to conclude that there is a linear correlation.
To determine if there is a linear correlation between the head widths and weights of seals, we need to compare the given correlation coefficient to the critical values for a significance level of 0.01.
The critical values represent the threshold at which we would reject the null hypothesis that there is no linear correlation.
Since the linear correlation coefficient given is 0.948, we need to find the critical values that correspond to a significance level of 0.01.
Looking up the critical values in a statistical table or using a calculator, we find that the critical values for a significance level of 0.01 are approximately ±0.959.
Therefore, the correct answer is:
D) Critical values=±0.959; there is NOT sufficient evidence to conclude that there is a linear correlation.