C1: MATLAB Codes t1=[37.79 39.51 38.54 39.14 39.02 39.4 39.01 37.18] t2=[22.4 22.07 22.15 21.72 21.75 22.55 22.18 21.92]
T1=mean(t1)
T2=mean(t2)
V1=var(t1)
V2=var(t2)
S1=sqrt(V1)
S2=sqrt(V2)
MATLAB Answers
T1=38.6988
T2=22.0925
V1=0.6718
V2=0.0859
S1=0.8196
S2=0.2931
C2:
MATLAB Codes beta=0.98 alpha=1-0.98 z=icdf ('norm', alpha/2, 0, 1) hatmu=mean(t1); hatmu=mean(t2) s=std(t1); s=std(t2) n=length (t1); n=length (t2) margin=z*s/sqrt(8) MATLAB Answers alpha=0.02 z=2.3263 margin(t1)=0.6741; margin(t2)=0.2931
C3:
MATLAB Codes syms l s b T1 T2

l=0.0496; s=1.00; b=10; T1=0.0386988; T2=0.0220925;

g=((l^2)/(2*s*sind(b)))*((1/T2^2)-(1/T1^2))

MATLAB Answers

g=9.7835

C4:
MATLAB Codes for Partial Derivatives

g=((l^2)/(2*s*sin(b)))*((1/T2^2)-(1/T1^2))

gl=diff(g,l)

gs=diff(g,s)

gb=diff(g,b)

gT1=diff(g,T1)

gT2=diff(g,T2)

MATLAB Answers for Partial Derivatives

gl=-(l*(1/T1^2 - 1/T2^2))/(s*sin(b))

gs=(l^2*(1/T1^2 - 1/T2^2))/(2*s^2*sin(b))

gb=(l^2*cos(b)*(1/T1^2 - 1/T2^2))/(2*s*sin(b)^2)

gT1=l^2/(T1^3*s*sin(b))

gT2=-l^2/(T2^3*s*sin(b))

MATLAB Codes for Partial Derivative Values

gl0=subs(gl,[l s b T1 T2],[l0 s0 b0 T10 T20])

gs0=subs(gs,[l s b T1 T2],[l0 s0 b0 T10 T20])

gb0=subs(gb,[l s b T1 T2],[l0 s0 b0 T10 T20])

gT10=subs(gT1,[l s b T1 T2],[l0 s0 b0 T10 T20])

gT20=subs(gT2,[l s b T1 T2],[l0 s0 b0 T10 T20])

MATLAB Answers for Partial Derivative Values

gl0= -125.9202

gs0= 3.1228

gb0= 4.8165

gT10= -78.0288

gT20= 419.3851

MATLAB Codes for Finding Uncertainties for g

g=9.7835; gl0= -125.9202; gs0= 3.1228; gb0= 4.8165; gT10= -78.0288; gT20= 419.3851

Wl=0.0005; Ws=0.002; Wb=0.3; WT1=0.6741; WT2=0.2931

Wg=sqrt((gl0*Wl)^2+(gs0*Ws)^2+(gb0*Wb)^2+(gT10*WT1)^2+(gT20*WT2)^2)

fprintf('The value of g is %f and its uncertainty is %f/n', g, Wg)