Question

From a sample of size 50, we have that Sxx=450 and Syy=800. Having tested the hypothesis that there is a negative relationship between two variables (i.e., H0:β1≤0), we obtain a p-value of 0.01186.

A. calculate the slope

Answer 1

Sample size,n = 50 Sxx= 450 (SSx)

SYY= 800( SSy)

Here, H0: β1≤0 Ha: β1>0 So, right tail t test is used . p-value is 0.01186 corresponding t statistic for n-2 = 50-2 = 48 degrees of freedom is 2.336 .

As t=β / SE (β1) = 2.336.

Thus β = 2.336 *(SE( β1)) -------(1)

Now,   

where  

Thus

Therefore using (1) equation

Slope = (2.336) (0.1925 )

= 0.44968