Question

2. Provide a test of the null hypothesis that the population correlation coefficient for X1-Y1 sample is zero against the alternative hypothesis that it is not zero. Set alpha=0.01.

a. Test statisitc ==>

b. Test critical value ==>

c. Conclusion ==>

3. Provide a test of the null hypothesis that the population correlation coefficients for the X2-Y2 and X3-Y3 samples are equal to one another versus the alternative hypothesis that the population correlation for the X3-Y3 sample is larger. Set alpha=0.1.

a. Test statisitc ==>

b. Test critical value ==>

c. Conclusion ==>

4. Provide a test of the null hypothesis that the population correlation coefficients are jointly equal across the three samples versus the alternative hypothesis that at least one of the three is different. Set alpha=0.05.

a. Test statisitc ==>

b. Test critical value ==>

c. Conclusion ==>

Data:

X1	Y1		X2	Y2		X3	Y3
36.69231	35.8		41.27072	52.4		45.80357	43.1
35.53846	47.7		39.74026	42.9		45	47.4
34.95868	37.6		36.11842	44.3		43.35079	50.5
34.73684	33.3		36	32.2		41.36646	44.2
34.54976	40.8		35.78947	38.1		39.58115	39.8
34.41176	41.3		35.30172	37.9		39.31579	41.5
33.66412	24.4		35	45.8		39	46
33.42857	34		34.90909	43.3		38.91892	39.8
33.33333	34.5		34.86911	31		38.86364	41.8
32.98429	35.3		34.5	34.8		38.8125	48.5
32.9771	35.6		34.44444	38.3		38.62069	45.7

Answer 1

SOLUTION 2]

X Values
∑ = 377.275
Mean = 34.298
∑(X - Mx)2 = SSx = 13.536

Y Values
∑ = 400.3
Mean = 36.391
∑(Y - My)2 = SSy = 337.689

X and Y Combined
N = 11
∑(X - Mx)(Y - My) = 27.706

R Calculation
r = ∑((X - My)(Y - Mx)) / √((SSx)(SSy))

r = 27.706 / √((13.536)(337.689)) = 0.4098

a] TEST STATISTIC t = r*sqrt(n-2)/sqrt(1-r^2)

t= 0.4098*sqrt(11-2)/sqrt(1-0.167936)

t= 1.3478

b] Degrees of freedom= n-2=11-2=9

t critical= 3.2498

c] Since t calculated SMALLER THAN t critical therefore NOT SIGNIFICANT

DECISION: DO NOT REECT H0.

CONCLUSION: WE DO NOT HAVE SUFFICIENT EVIDENCE TO CONCLUDE THAT THE POPULATION CORRELATION COEFFICIENT IS NOT ZERO AT 0.01 LEVEL OF SIGNIFICANCE

NOTE: AS PER Q&A GUIDELINES I HAVE DONE THE FIRST QUESTION PLEASE RE POST THE REST. THANK YOU