Question

The following data show the rankings of  states based on expenditure per student (ranked  highest to  lowest) and student-teacher ratio (ranked  lowest to  highest). Use Table 1 of Appendix B.

State	Expenditure per Student	Student-Teacher Ratio
Arizona	10	10
Colorado	6	9
Florida	5	6
Idaho	3	10
Iowa	6	4
Louisiana	10	3
Massachusetts	1	1
Nebraska	8	2
North Dakota	9	8
South Dakota	11	5
Washington	3	9

a. What is the rank correlation between expenditure per student and student-teacher ratio (to 2 decimals). Enter negative values as negative numbers.

rs= ?  

b. At the  level, does there appear to be a relationship between expenditure per student and student-teacher ratio?

z= ?  

c. p-value is ? (to 4 decimals)

d. Conclusion:
- Select your answer -We can conclude that there is a significant relationship.We cannot conclude that there is a significant relationship.Item 4

Answer 1

SOLUTION-

A.)

STATE	EXPENDITURE(X)	STUDENT-TEACHER RATIO(Y)	D=X-Y
ARIZONA	10	10	0	0
COLORADO	6	9	-3	9
FLORIDA	5	6	-1	1
IDAHO	3	10	-7	49
LOWA	6	4	2	4
LOUSIANA	10	3	7	49
MASSACHUSSETS	1	1	0	0
NEBRASKA	8	2	6	36
NORTH DAKOTA	9	8	1	1
SOUTH DAKOTA	11	5	6	36
WASHINGTON	3	9	-6	36
TOTAL				221

THE SPEARMAN'S RANK CORRELATION IS DEFINED AS,

HERE, n=11, HENCE THE CORRELATION COEFFICIENT IS,

B.) IN ORDER TO TEST IF THERE IS A RELATIONSHIP BETWEEN THE SAMPLES, WE FRAME THE GIVEN HYPOTHESIS,

THE TEST STATISTIC IS,

HENCE, THE TEST STATISTIC IS,

C.) THE P-VALUE OBTAINED IS 0.9906

[CALCULATED FROM P-VALUE CALCULATOR FOR A T-TEST]

D.) AS P-VALUE> LEVEL OF SIGNIFICANCE, WE FAIL TO REJECT THE NULL HYPOTHESIS. HENCE WE CONCLUDE THAT THERE IS SIGNIFICANT RELATIONSHIP AT 5% LEVEL OF SIGNIFICANCE.

**** IN CASE OF DOUBT, COMMENT BELOW. ALSO LIKE THE SOLUTION, IF POSSIBLE.