Find the standardized test statistic t for a sample with n = 15,x- (x bar) = 4.5, s = 0.8, and ? = 0.05 ifH0: ? <_ (less than or equal to) 4.2. Round youranswers to three decimal places. a. 1.452 b. 1.312 c. 1.728 d. 1.631 Solution t = (xbar - mu) / (stdev/sqrt(n)) t = (4.5 - 4.2) / (0.8/sqrt(15)) t = 1.452 Ans) a 1.452.

1. Find the unit vectors u that are perpendicular to both i+2j+k and 3i-4j+2k.
Solution
a=i+2j+k
b=3i-4j+2k
now the cross product axb is perpendicular to both a and b
axb = i j k
1 2 1
3 -4 2
=8i+j-10k
axb=(8^2+1^2+(-10^2))^0.5=(64+1+100)^0.5=165^0.5=12.845
so a unit vector perpendicular to both a and b is a unit vector along axb
now unt vector along axb is
c = axb/(axb)=(8i+j-10k)/12.845=0.623 i +0.07785 j -0.7785 k ans