Question

Managers rate employees according to Job Performance and Attitude. The results for several randomly selected employees are given below: Performance X | 60 | 63 65 Attitude Y 72 67 78 71 | 57 | 79 | 80 | 69 | 70 | 63 82 75 87 92 82 88 78 Test the claim that the population correlation coefficient p > 0. Use a=.01. Be sure to include the statements of the null and alternative hypotheses, the Test used, the relevant P-value, whether or not to Reject Ho and why, and the conclusion in words for this problem. (10 pts)

Answer 1

We need to test the claim that the population correlation coefficient 830 Hence the hypotheses for the test are: Null hypothesis ; Hoisso Aktemative hypothesis ; H:850 This corresponds to a t-test for correlation coesficient; which is right Sided test as we are testing if a greater than o. Test statistics : 8 * Jn-2 where re sample worselation coefficient 11-72 ne sample size = 10. So we need to calculate the sample correlation coefficient of in order to calculate ite test statistics G-8² (x-7)(y-7) t (y-7)? X Y Y-7 X-5 72 65-61 59.29 -8.1 -7.7 62-37 61.57 -13) 22.09 171-61 63 67 -407 4.41 5.67 -2.1 65 78 - 2-7 7.29 10.89 3.61 6-27 71 32 3.3 1-9 54.57 26.01 114-49 57 -51 75 -1007 77.97 79 11.3 6.9 127-69 47.61 87 146.37 11.9 151-29 141.61 80 92 12-3 3.61 2.47 1-69 1.9 69 82 1.3 62.41 18:17 7.9 5.29 70 88 2.3 4.41 9-87 22-09 -2.1 -4-7 78 522.10 530.90 445-30 63 677 801 445.30 ř=677-67.7 Y = lo Ex-x)(y-7) JER-K) ² {(7-77² 522-1 * 530.9 Y = 801 - 80.1 = 0.8458 0.8458* 2-8284 = 4.484 ata 0.8458 /10-2 JI-6=8458) 0.5335

P-value : As this is a night tailed test the p-value = P(T>+) for degrades of freedom - N-2 je p-value = PCT >4.484) for 8 degmes of freedom VO001 (foom T distribution table). Decision about the null hypothesis As the p-value = 0.001 is less than the significance level 0.01; the nule hypothesis is rejected. Conclusion Since the nuce hypothesis is rejected ; there is sufficient evidence to support the claim that the population Correlation coefficient S so; at the significance level '=0.01.