Find the square roots of the complex number [-80-18i ] and solve the following quadratic equation. [4z^2+(16i-4)z+(65+10i) = 0] Solution Let [sqrt(-80-18i)=a+ib] squaring both side [-80-18i=a^2-b^2+2abi] coparing real and magnary parts both side [a^2-b^2=-80] [2ab=-18] But [(a^2+b^2)^2=(a^2-b^2)^2+4a^2b^2] [(a^2+b^2)=(-80)^2+(-18)^2] [=6400+324=6724] [a^2+b^2=+-82] Now solve [a^2-b^2=-80] [a^2+b^2=+-82] [If] [a^2-b^2=-80] [a^2+b^2=82] [Then] [a=+-1 and b=+-9] [if] [a^2-b^2=-80] [a^2+b^2=-82] [a=+-9 and b=+-1] [Thus] [sqrt(-80-18i)=+-1+-9i] [or] [sqrt(-80-18i)=+-9+-i] [4z^2+(16i-4)z+(65+10i)=0] [z=(-(16i-4)+-sqrt((16i-4)^2-16(65+10i)))/8] [=(-(16i-4)+-sqrt(-256+16-128i-1040-160i))/8(] [=(-(16i-4)+-sqrt(-1280-288i))/8] [=(-(4i-1)+-sqrt(-80-18i))/2] [Thus] [z=(-4i+1+-1+-9i)/2] [and] [z=(-4i+1+-9+-i)/2].

1. Find the statement that is correct.
Question 12 options:
A) Sample statistics come from a specific statistical procedure, while test statistics are
associated with the observed data.
B) One of the reasons why we use the null hyposthesis is based on Ronald Fisher's
philosophical argument that it is easy to prove something to be true whereas it is hard to prove
something to be false.
C) Mostly, the standard error and the standard deviation of the population distribution have the
same value.
D) Sampling distributions help us test hypotheses about means by telling us what kinds of
means to expect if the null hypothesis is true.
Solution
D) Sampling distributions help us test hypotheses about means by telling us what
kinds of means to expect if the null hypothesis is true.