Question

(2 points) For the data set (-2,-3).(3,3), (6,4), (9,7).(11,10), carry out the hypothesis test H. Ⓡ, = 0 HB10 Determine the value of the test statistic and the associated p-value. Test Statistic = p-Value = Note: In order to get credit for this problem all answers must be correct

Please answer ASAP

Answer 1

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	27.00	21.00	105.20	94.80	98.60
mean	5.40	4.20	SSxx	SSyy	SSxy

Sample size,   n =   5      
here, x̅ = Σx / n=   5.400          
ȳ = Σy/n =   4.200          
SSxx =    Σ(x-x̅)² =    105.2000      
SSxy=   Σ(x-x̅)(y-ȳ) =   98.6      
              
estimated slope , ß1 = SSxy/SSxx =   98.6/105.2=   0.9373      
intercept,ß0 = y̅-ß1* x̄ =   4.2- (0.9373 )*5.4=   -0.8612      
              
Regression line is, Ŷ=   -0.9   + (   0.937   )*x

Ho:   β1=   0
H1:   β1╪   0
n=   5  

estimated std error of slope =Se(ß1) = Se/√Sxx =    0.8918/√105.2=   0.0869
t stat = estimated slope/std error =ß1 /Se(ß1) =    (0.9373-0)/0.0869=   10.78
Degree of freedom ,df = n-2=   3  
      
p-value =    0.0017  
decison :    p-value<α , reject Ho  
Conclusion:   Reject Ho and conclude that slope is significantly different from zero  

Please let me know in case of any doubt.

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