A shipping company believes there is a linear association between the weight of packages shipped and the cost.The following table shows the weight (in pounds)and cost (in dollars)of the last seven packages shipped. Using the critical value approach and α = 0.10,the appropriate conclusion is _________.
A) do not reject the null hypothesis;conclude weight and cost are correlated
B) do not reject the null hypothesis;we cannot conclude the correlation coefficient is different from zero
C) reject the null hypothesis;we cannot conclude the correlation coefficient is different from zero
D) reject the null hypothesis;conclude weight and cost are correlated

Question

A shipping company believes there is a linear association between the weight of packages shipped and the cost.The following table shows the weight (in pounds)and cost (in dollars)of the last seven packages shipped.  Using the critical value approach and α = 0.10,the appropriate conclusion is _________.
A) do not reject the null hypothesis;conclude weight and cost are correlated 
B) do not reject the null hypothesis;we cannot conclude the correlation coefficient is different from zero 
C) reject the null hypothesis;we cannot conclude the correlation coefficient is different from zero 
D) reject the null hypothesis;conclude weight and cost are correlated

Quizplus · Accepted Answer

We need to perform a hypothesis test to determine whether there is a significant linear association between weight and cost. The null hypothesis is that there is no correlation between weight and cost (i.e., the correlation coefficient is zero) and the alternative hypothesis is that there is a correlation between weight and cost.

We use the critical value approach with a significance level (α) of 0.10. Using a table of critical values for the Pearson correlation coefficient, we find that the critical value for a two-tailed test with n = 7 and α = 0.10 is 0.524.

We calculate the sample correlation coefficient to be r = 0.982. Since this value is greater than the critical value of 0.524, we reject the null hypothesis and conclude that there is a significant linear association between weight and cost. Therefore, the best choice is D.

A Shipping Company Believes There Is a Linear Association Between