Advanced High-School Mathematics

SECTION 6.4 Confidence Intervals 389

PROGRAM: CONFINT1

:0→C

:Input ”POP MEAN ”, M

:Input ”POP STD ”, S

:Input ”NO OF EXPER ”, N

:5→K

:For(I,1,100)

:randNorm(M,S,K)→L 1

:mean(L 1 )→X

:(K/(K-1))(mean(L^21 )−X^2 )→V

:2. 776

»

V/K→Q

:X−Q→L

:X + Q→U

:C+ (L≤2)(2≤U)→C

:END

:Disp C

:Stop

(f) In the above program, change the commands as follows

Input ”POP MEAN ”, M to 1/ 3 →M

randNorm(M,S,K)→L 1 to rand(K)^2 →L 1

Input ”POP STD ”, S to anything (it’s now irrelevant)

Notice that this time we are taking small samples from a

highly non-normal population (rand^2 ). Are we still capturing

the true mean (= 1/3) roughly 95% of the time?

6.4.3 Confidence interval for a population proportion

Professional pollsters love to estimate proportions: in any political race
and at virtually any time, they will take samples from the voting pop-
ulation to determine whether they prefer candidate A or candidate B.
Of course, what the pollsters are trying to determine is the overall
preference—as a proportion—of the entire population. I seem to re-
member reading sometime during the 2004 U.S. presidential campaign