Spikegraph:=proc(distributionlist,xmin,xmax,show,c)
local num,linelist,j,i,templist:
templist:=[]:
if ((distributionlist[1][1]<xmin) or
(distributionlist[nops(distributionlist)][1]>xmax)
) then
lprint(`Note: some data values lie outside the user-defined interval.`)
fi:
for i from 1 to nops(distributionlist) do
if not((distributionlist[i][1]<xmin) or (distributionlist[i][1]>xmax)) then
templist:=[op(templist),
[distributionlist[i][1],
distributionlist[i][2]
]
]:
fi:
od:
num:=nops(templist):
linelist:=[]:
for j from 1 to num do
linelist:=[op(linelist),[templist[j][1],0]]:
linelist:=[op(linelist),[templist[j][1],templist[j][2]]]:
linelist:=[op(linelist),[templist[j][1],0]]:
od:
if show then plot(linelist,style=LINE,color=c) fi;
end:
Bin:=proc(n,p,k)
(binomial(n,k))*(p^k)*((1-p)^(n-k));
end:
with(plots):
BinomialPlot:=proc(n,p,q)
local length,i,j1,j2,j3,j4,j5,spikelist1,spikelist2,spikelist3,
spikelist4,spikelist5,A1,A2,A3,A4,A5:
spikelist1:=[]:
spikelist2:=[]:
spikelist3:=[]:
spikelist4:=[]:
spikelist5:=[]:
for j1 from 0 to floor(n*(p-q))
do
spikelist1:=[op(spikelist1),[j1,Bin(n,p,j1)]] ;
od:
for j2 from ceil(n*(p-q)) to floor(n*(p+q)) do
spikelist2:=[op(spikelist2),[j2,Bin(n,p,j2)]] ;
od:
for j3 from ceil(n*(p+q)) to n do
spikelist3:=[op(spikelist3),[j3,Bin(n,p,j3)]] ;
od:
A1:= Spikegraph(spikelist1,0,floor(n*(p-q)) ,true,blue);
A2:=Spikegraph(spikelist2,ceil(n*(p-q)),floor(n*(p+q)),true,red);
A3:=Spikegraph(spikelist3,ceil(n*(p+q)) , n,true,blue);
display(A1,A2,A3);
end:
Conf:=proc(n,p,q)
local r,s;
r:=sum(
binomial(n,k)*(p^k)*((1-p)^(n-k)),k=ceil(n*(p-q))...floor(n*(p+q))
);
evalf(r);
end:
"Here we have a program which does a confidnce analsis. To be completely honest since you don't know p you should use p=1/2.":
Confidence:=proc(n,p,q)
local r;
lprint("You are",100*Conf(n,p,q) ,"percent confidence that your measured percntage is with in ", 100*q,"percent of the true percent");
BinomialPlot(n,p,q);
end:"Now we will explore the above program. It computes the confidence of a the true percentage lies within plus or minus 100q percent of a randomly sampled percentage, given you performed n random trials. In order to be completely safe you would plug into Confidence(n,p,q) the above information for n and q along with and p=1/2. This means you are using the 'non-exaggeration' method. The 'exaggeration method' allows you to plug in for p your MEASURED percent. As we discussed, both are reportable (in the socially acceptable sense) but using p=.5 is more honest.":Confidence(65,.5,.1);