Fill in the blank. The critical value tα/2 that corresponds to a % confidence level with 1000 degrees of freedom is 2.33.

The critical value tα/2 that corresponds to a 98% confidence level with 1000 degrees of freedom is 2.33.

Step-by-step explanation:

From the question we are told that

   The critical value is  

From the student's t distribution table the probability of     at a degree of freedom of  1000 is  

Hence the level of significance is mathematically evaluated as

=>    

Generally the confidence level  is mathematically represented as

=>  

=>  

Converting to  percentage

=>    

=>    

system of linear equation

step-by-step explanation:

as given in the data

a= 20 , b= -12

let us suppose that it is a straight line equation

now we know the formula for the system of linear equation

b= ma + c )

here m is slope of a straight line which is equal to formula

m=   (ii)

and here c is a constant

now putting the value of a and b in equation (ii)

m=

m=

putting the value of a,b and m in equation (i) gives us

-12 = + c

-12=-12 + c

adding 12 to both sides

-12 +12 = -12 +12 +c

0 =c

or c=0

as the value of the constant is zero which gives us that it is a linear equation and this order pair satisfies the system of linear equations.