Page 58 - Statistics II for Dummies

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Part I: Tackling Data Analysis and Model-Building Basics
Every margin of error is interpreted as plus or minus a certain number of
standard errors. The number of standard errors added and subtracted is
determined by the confidence level. If you need more confidence, you add
and subtract more standard errors. If you need less confidence, you add and
subtract fewer standard errors. The number that represents how many standard
errors to add and subtract is different from situation to situation. For one
population mean, you use a value on the t-distribution, represented by t ,
n – 1
where n is the sample size (see Table A-1 in the appendix).
Suppose you have a sample size of 20, and you want to estimate the mean of a
population with 90 percent confidence. The number of standard errors you
add and subtract is represented by t , which in this case is t = 1.73. (To find
n – 1 19
these values of t, see Table A-1 in the appendix, with n – 1 degrees of freedom
for the row, and for the column.)

Now suppose you want to be 95 percent confident in your results, with the
same sample size of n = 20. The degrees of freedom are 20 – 1 = 19 (row) and

the column is for . The t-table gives you the value of t = 2.09.
19
Notice that this value of t is larger than the value of t for 90 percent confidence,
because in order to be more confident, you need to go out more standard
deviations on the t-distribution table to cover more possible results.

Large confidence, narrow intervals — just the right size
A narrow confidence interval is much more desirable than a wide one. For
example, claiming that the average cost of a new home is $150,000 plus
or minus $100,000 isn’t helpful at all because your estimate is anywhere
between $50,000 and $250,000. (Who has an extra $100,000 to throw around?)
But you do want a high confidence level, so your statistician has to add and
subtract more standard errors to get there, which makes the interval that
much wider (a downer).

Wait, don’t panic — you can have your cake and eat it too! If you know you
want to have a high level of confidence but you don’t want a wide confidence
interval, just increase your sample size to meet that level of confidence.

Suppose the standard deviation of the house prices from a previous study is
s = $15,000, and you want to be 95 percent confident in your estimate of aver-
age house price. Using a large sample size, your value of t (from Table A-1 in
the appendix) is 1.96.

With a sample of 100 homes, your margin of error is .
If this is too large for you but you still want 95 percent confidence, crank up

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