Question

Sarah is the office manager for a group of financial advisors who provide financial services for individual clients. She would like to investigate whether a relationship exists between the number of presentations made to prospective dients in a month and the number of new clients per month. The accompanying table shows the number of presentations and corresponding new clients for a random sample of six employees Sarah would Relo se simple regression analysis to estimate the number of new clients per month based on the number of presentations made by the employee per month. Which one of the following statements descrbes the results of the hypothesis test that the population correlation coeficient is greater than zero using a 0.107 Click the icon to view the results for the random sample OA. Because the testatistic is greater than the critical value, we fail to reject the rull hypothesis and conclude that the population correlation coefficient is greater than 200 O B. Because the lost statistic is less than the critical value, we fail to reject the nul hypothesis and cannot conclude that the population correlation coefficient is greater than zero OC. Because the test statistic is less than the critical value, we can reject the nul hypothesis and conclude that the population correlation coefficient is not greater than zero OD. Because the test statistic is greater than the critical value, we can reject the null hypothesis and conclude that the population correlation coeficient is prefer than zero random sample results Employee 1 2 3 4 Presentations 7 9 New Clients 2 3 10 11 12 5 6 3 Print Done

Answer 1

To test the significance of correlation coefficient we have to first calculate the correlation coefficient.

In excel we can calculate the correlation coefficient by using the formula =CORREL(array1,array2)

But if you don't want to use excel you can use the formula as follows

$r=\frac{\frac{\sum XY}{n}-\bar X\bar Y}{\sqrt{(\frac{\sum X^{2}}{n}-\bar X^{2})(\frac{\sum Y^{2}}{n}-\bar Y^{2})}}$

fx А B с D D G 1 S.No. Xi Yi Xi2 XIYi 2 4 7 9 w NP Yi2 49 81 81 14 27 3 2 3 9 4 9 4 16 36 5 4 10 3 9 6 5 100 121 144 11 12 58 7 5 3 20 6 30 55 36 198 25 9 72 8 Total 576 9 10 11 mean of x = mean of Y = 9.6666667 3.3333333 12 13 14 correlation coefficient = 0.516046847 15

Given Y = 0.10 and data 2 Employce Presentation New Clients 7 2 9 3 3 g 4 + 16 3 5 !! 5 12 3 6 We have calculated correlation coefficient using Excel formula '= = CORREL(array L, azsay2) that is r=0.516 New Alternative Mypothesia Null Hypothesis , Ho : f=0 ie (There is no correlation) 170 (Right tailed test) Test statistic under Ho s: में 8Jn-2 T-22 wtra t = 0.516 Jo-q 1.032 JI -0.266 0.8567 t 1.205 ~t4 critical value of toto for 4 af is 1.53]. Conclusion: Because the test statistic is less than the critical value, we fail to reject the null hypothesis and cannot conclude that the population correlation greater them Tero . Cotton B Coefficient is
option B is correct