Exhibit 20.9.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 7 packages shipped. Refer to Exhibit 20.9.Using the critical value approach,the appropriate conclusion is:
A)Do not reject the null hypothesis,conclude weight and cost are correlated
B)Do not reject the null hypothesis,cannot conclude the is different from zero
C)Reject the null hypothesis,cannot conclude the correlation coefficient is different from zero
D)Reject the null hypothesis,conclude weight and cost are correlated

Question

Exhibit 20.9.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 7 packages shipped.  Refer to Exhibit 20.9.Using the critical value approach,the appropriate conclusion is:
A)Do not reject the null hypothesis,conclude weight and cost are correlated 
B)Do not reject the null hypothesis,cannot conclude the is different from zero 
C)Reject the null hypothesis,cannot conclude the correlation coefficient is different from zero 
D)Reject the null hypothesis,conclude weight and cost are correlated

Quizplus · Accepted Answer

Using the critical value approach, we compare the calculated t-statistic with the critical value at the desired level of significance for n-2 degrees of freedom. The calculated t-statistic is 2.1703, and the critical value at a 0.05 level of significance for 5 degrees of freedom is 2.571. Since the calculated t-statistic is less than the critical value, we do not reject the null hypothesis. Therefore, we cannot conclude that the correlation coefficient is different from zero. Alternatively, the p-value approach gives a p-value of 0.0732, which is greater than the chosen level of significance of 0.05. Thus, we fail to reject the null hypothesis and cannot conclude a relationship between weight and cost. However, if we chose a higher level of significance, such as 0.10, we would reject the null hypothesis and conclude that weight and cost are correlated. However, since the question asks for the appropriate conclusion using the critical value approach at a 0.05 level of significance, the correct answer is D. We reject the null hypothesis and conclude that weight and cost are correlated.