97.35% Chance That Huckabee Will Win Iowa

The latest polls listed on the RealClearPolitics website list the following numbers:

American Res. Group (12/31 - 01/02) Huckabee 29%, Romney 24% (600 Likely Voters)
Zogby Tracking (12/30 - 01/02) Huckabee 31%, Romney 25% (914 Likely Voters)
InsiderAdvantage (01/01 - 01/01) Huckabee 30%, Romney 24% (430 Likely Voters)
Strategic Vision (12/28 - 12/30) Huckabee 28, Romney 30% (600 Likely Voters)
Des Moines Register (12/27 - 12/30) Huckabee 32%, Romney 26% (800 Likely Voters)
CNN (12/26 - 12/30) Huckabee 28%, Romney 31% (373 Likely Voters)

The weighted average for these polls is Huckabee 29.99%, Romney 26.35%, with the aggregate sample size equalling 3,717 voters.

Let's calculate the margin of error for Mike Huckabee. This equals 1.96 X Square Root (29.99% x 70.01% / 3,717), or 1.47%. (The standard deviation is 0.0075). As such, Mike's range is 28.52% to 31.46%.

Let's calculate the margin of error for Mitt Romney. This equals 1.96 X Square Root [26.35% x 73.65% / 3,717], or 1.42%. (The standard deviation is 0.0072). As such, Mitt's range is 24.93% to 27.76%.

Notice that Mitt's high range (27.76%) is LOWER than Mike's low range (28.52%). Mike is leading outside of the margin of error with only seven hours to caucus.

What is the probability of Mike's true average exceeding Mitt's true average?

STEP 1: The probability of Mike's true average exceeding Mitt's high range number is based upon the normal distribution. The cumulative normal distribution will take Mitt's high range (we will call it "x"), Mike's sample average (we will call it "u"), and Mike's standard deviation (call it "sd").

The probablity of Mike's true average exceeding Mitt's high range is equal to 1-cumulative normal distribution with the aforesaid values for x, u, and sd. From the EXCEL spreadsheet function, this value equals 1- NORMDIST (0.2776, 0.2999, 0.0075, TRUE), or .998527.

STEP 2: Since the augmented poll has a confidence interval of 95% (hence the Z-value of 1.96), there is a 2.5% chance that Romney's true average exceeds his high range. Put in terms favorable to Mike, there is a 97.5% chance that Mitt's true average will be less than his high range value.

STEP 3: The probability of Mike winning is .998527 x .975, or .9735

FINAL ANSWER --- MIKE HUCKABEE HAS A 97.35% CHANCE OF WINNING.