Question

Use the data set attached.

Include your SPSS output in this document as part of Step 3.

Test for the significance of the correlation coefficient at the .05 level using a two-tailed test between hours of studying and grade.

Hours of Study Grade

0 80

5 93

8 97

6 100

5 75

3 83

4 98

8 100

6 90

2 78

Answer 1

x	y	(x-x̅)²	(y-ȳ)²	(x-x̅)(y-ȳ)
0	80	22.09	88.36	44.18
5	93	0.09	12.96	1.08
8	97	10.89	57.76	25.08
6	100	1.69	112.36	13.78
5	75	0.09	207.36	-4.32
3	83	2.89	40.96	10.88
4	98	0.49	73.96000	-6.0200
8	100	10.89	112.36000	34.980
6	90	1.69	0.36	0.78
2	78	7.29	129.96	30.78

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	47.00	894.00	58.10	836.40	151.20
mean	4.70	89.40	SSxx	SSyy	SSxy

correlation coefficient ,    r = Sxy/√(Sx.Sy) =   0.6859

correlation hypothesis test   tail=   2
Ho:   ρ = 0  
Ha:   ρ ╪ 0  
n=   10  
alpha,α =    0.05  
correlation , r=   0.6859  
t-test statistic = r*√(n-2)/√(1-r²) =        2.666
DF=n-2 =   8  
p-value =    0.0285  
Decison:   p value < α , So, Reject Ho  
so, correlation is significant