Page 202 - Statistics for Dummies

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Part IV: Guesstimating and Hypothesizing with Confidence
is at least 10.

1. You need to be sure that
2. You need to make sure that
is at least 10.

In the preceding example of a poll on the president, n = 1,000, = 0.52, and
= 1,000 ∗ 0.52 = 520, and
is 1 – 0.52 = 0.48. Now check the conditions:
= 1,000 ∗ 0.48 = 480. Both of these numbers are at least 10, so every-
thing is okay.
Most surveys you come across are based on hundreds or even thousands of
people, so meeting these two conditions is usually a piece of cake (unless the
sample proportion is very large or very small, requiring a larger sample size
to make the conditions work).
A sample proportion is the decimal version of the sample percentage. In other

words, if you have a sample percentage of 5%, you must use 0.05 in the for-
mula, not 5. To change a percentage into decimal form, simply divide by 100.
After all your calculations are finished, you can change back to a percentage
by multiplying your final answer by 100%.
Reporting results
Including the margin of error allows you to make conclusions beyond your
sample to the population. After you calculate and interpret the margin of
error, report it along with your survey results. To report the results from
the president approval poll in the previous section, you say, “Based on my
sample, 52% of all Americans approve of the president, plus or minus a
margin of error of 3.1%. I am 95% confident in these results.”
How does a real-life polling organization report its results? Here’s an example
from Gallup:
Based on the total random sample of 1,000 adults in (this) survey, we are
95% confident that the margin of error for our sampling procedure and its
results is no more than ±3.1 percentage points.
It sounds sort of like that long list of disclaimers that comes at the end of a
car-leasing advertisement. But now you can understand the fine print!
Never accept the results of a survey or study without the margin of error for
the study. The MOE is the only way to estimate how close the sample statistics
are to the actual population parameters you’re interested in. Sample results
vary, and if a different sample had been chosen, a different sample result would
have been obtained; the MOE measures that amount of difference.

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