Question

To identify high-paying jobs for people who do not ke stress, suppose the following data were collected sho teci Day to answer this ($1,000s) and the stress tolerance for a variety of occupations Job Average Annual Salary ($1,000s) Stress Tolerance Art directors 81 69.0 Astronomers 96 62.0 Audiologists 70 67.5 Dental hygienists 70 70.3 Economists 92 Engineers 69.5 92 62.8 Law teachers 100 65.5 Optometrists 98 102 60.1 Political scientists Urban and regional planners 65 69.0 The stress tolerance for each job is rated on a scale from 0 to 100, where a lower rating indicates less stress. (a) Develop a scatter diagram for these data with average annual salary as the independent variable. 757 75 70 70+ 65 65 Stress Tolerance Stress Tolerance 60 60 55+ 55+ 50 110 50 110 60 70 80 90 100 Average Annual Salary($1,000s) 60 70 BO 90 100 Average Annual Salary($1,000s) O 0 75 75 70 70 65 65+ Stress Tolerance Stress Tolerance 60+ 60 55+ 55+ 50 110 50 110 60 70 BD 90 100 Average Annual Salary($1.000) 60 70 80 90 100 Average Annual Salary($1.000s)

pleass help im stuck on this question

Answer 1

a) The correct scatter plot from the given plots is

18 70 . 65 Stress Tolerance 60+ 55 50 60 70 80 90 100 110 Average Annual Salary ($1,000s)

Interpretation: There appears to be a negative linear relationship between average salary ($ 1,000) and stress tolerance.

	Average Annual Salary (x)	Stress Tolerance (y)	(x-Mx)^2	(y-My)^2	(x-Mx)(y-My)
1	81	69	31.36	9.61	-17.36
2	96	62	88.36	15.21	-36.66
3	70	67.5	275.56	2.56	-26.56
4	70	70.3	275.56	19.36	-73.04
5	92	63.3	29.16	6.76	-14.04
6	92	69.5	29.16	12.96	19.44
7	100	62.8	179.56	9.61	-41.54
8	98	65.5	129.96	0.16	-4.56
9	102	60.1	237.16	33.64	-89.32
10	65	69	466.56	9.61	-66.96
Total	866	659	1742.4	119.48	-350.6

n= 10 10 - 86.6 X=Mx = tri = 866 7 = My = h Ey; = 659 = 65.9 Syst={phim = 1742,4 Syy=2g-my)² = 119,48. Say - E-ma) (my) = -350.6 b) Stope (6)= Sxy = -0.2012 Intercept (bg) = My- b Ma = 83.3254 The regression equation is û = 83.325 -0,201 e) The null and alternative hypothesis sar HoiB=0 Harß,70 ) Ss Treat = SS Error = The value 11,533 Sny =48.933 Syyn Suy sex = 70.547 San of test statistic, SS Treat / SS Ever/m=2) prvalue = 0.009 (P-value for F=11.533 with (18) df) Conclusion, Reject Ho, we conclude that the relationship between average annual salary ($1,000) and stress tolerance significant. d) since ² Sey -0.5904 is greater than 0.60, the es San Syg we estimated regression equation is god fit. Therefore, feel can feel comportable wring the estimated estimate the shess level tobronce given the average annual average annual salary is within the range of the current dara regression equation to salary if the value of the

e) Yes, the relationship between average annual salary and sress tolerance for these data seem reasonable because the the slope is significant by using F-test statistic .