Question

Please show all work and state null and research hypotheses in complete sentences

Correlation Hypothesis Testing
Person       X (exercise- hr per week)         Y (stress level)
1                               5                                        4
2                               7                                        2
3                               6                                        0
4                               3                                        7
5                               6                                        5
6                               4                                        4
7                               4                                        6
                               x̅=5                   (underline dash - on top of Y) Y=4

Q1: State your null and research hypotheses.
Q2: What are the cut-off points?
Q3: What is SSx?
Q4: What is SSy?
Q5: What is SP?
Q6: What is r?
Q7: Write your conclusion thoroughly.

Answer 1

1)

null hypothesis: Ho:           ρ'=		0
Alternate Hypothesis: Ha: ρ≠		0

2)

0.05 level,two tail test and n-2= 5 df, critical r=± 0.754

3)

S.No	X	Y	(x-x̅)2	(y-y̅)2	(x-x̅)(y-y̅)
1	5	4	0.0000	0.00	0.0000
2	7	2	4.0000	4.00	-4.0000
3	6	0	1.0000	16.00	-4.0000
4	3	7	4.0000	9.00	-6.0000
5	6	5	1.0000	1.00	1.0000
6	4	4	1.0000	0.00	0.0000
7	4	6	1.0000	4.00	-2.0000
Total	35	28	12.0000	34.0000	-15.0000
Mean	5.000	4.00	SSX	SSY	SXY

SSx =12

4)

SSy =34

5)SP =-15

6)

correlation r='Sxy/(√Sxx*Syy) =

-0.743

7)

since test statistic does not falls in rejection region we fail to reject null hypothesis

we do not have have sufficient evidence to conclude that there is significant correlation between two variables