when 30 bolts are tested for hardness, their indexes have a standard deviation of 3.9. Test the claim that the standard deviation of the hardness indexes for all such bolts is 6.1. use a 0.01 level of significance.

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the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below:

you could deduce the conclusion directly using the facts pertaining to the specific situation.

hope this .