Question

Managers rate employees according to job performance and attitude. The results for several randomly selected employees are given below. Performance (x) / 3 / 2 / 3 / 7 / 4 / 8 / 2 / 2 / 2 / 6 Attitude (y) / 2 / 2 / 1 / 7 / 7 / 6 / 2 / 8 / 5 / 4 Use the given data to find the test statistic for testing linear correlation. Round the final values to three significant digits, if necessary.

Answer 1

First we need to calculate the correlation between Performance(x) and attitude(y)

We shall be using the formulae below:

where

we shall form the squares and cross product tables below:

	x	y
	3	2	9	4	6
	2	2	4	4	4
	3	1	9	1	3
	7	7	49	49	49
	4	7	16	49	28
	8	6	64	36	48
	2	2	4	4	4
	2	8	4	64	16
	2	5	4	25	10
	6	4	36	16	24
Total	39	44	199	252	192

Testing correlation coefficient:

Test statistic

  

  

  . The critical value of t at n-1=10-2=8 df is 2.306. Since the calculated value of t <teh critical value,we do not reject the null hypothesis. Hence we conclude that there is not enough evidence that there is linear relationship between performamnce and attitude.