Pinworm: In Sludge County, a sample of 50 randomly selected citizens were tested for pinworm. Of these, 10 tested positive (20%). The CDC reports that the U. S. average pinworm infection rate is 12%. Conduct the following hypothesis tests and finish with an understandable concluding statement. (a) Test the claim that Sludge County has a pinworm infection rate that is greater than the national average. Use a 0.05 significance level.
(b) Test the claim that Sludge County has a pinworm infection rate that is greater than the national average. Use a 0.01 significance level.
(c) Why was it that you could make apparently contradictory statements in parts (a) and (b)?

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step-by-step explanation:

the value of v.w= -12.

step-by-step explanation:

we are given three vector r,v and w as:

r = < 5, -5, -2> ; v = < 2, -8, -8> ; w = < -2, 6, -5>

we know that r,v and w could also be represented as:

r=5i-5j-2k

v=2i-8j-8k

and w= -2i+6j-5k

where i,j and k are the unit vectors of x,y and z-axis respectively.

also we know that it has the following property:

i.i=1 ; j.j=1; k.k=1

and i.=j.i=i.k=k.i=j.k=k.j=0

i.e. when we multiply two vectors or we find it's dot product we need to only multiply the components of x coordinates with each other; y with each other and z with each other.

hence, v.w= (2i-8j- -2i+6j-5k)

                  = 2×(-2)+(-8)×(6)+(-8)×(-5)

                  = -4-48+40

                  = -12

hence, v.w= -12