1. Estimating
Population Parameters
and
Margins of Error
2. Margin of Error
• Range of Values below and above sample
statistic in a confidence interval
– EX: suppose we wanted to know the percentage
of students who do their homework. Need to
construct a sample design (sampling method and
estimator) where the sample estimate will not
differ from the true population value by more
than 3% (margin of error) 95% of the time
(Confidence level)
3. How to compute the margin of
Error
• Given population attributes and the standard
deviation of the statistic
ME= Critical Value x Standard Deviation of Statistic
• Given sample attributes and know the
standard error of the statistic
ME= Critical Value x Standard Error of Statistic
= (t/z value) x (s/ √n)
***It is important to realize that the critical value can either be represented by a z* or
a t*. (Refer back to the “conditions” to know when to use which)
4. What is the Critical Value (CV)?
• Critical value is used to calculate the Margin of Error
• Sampling distribution must be normal
– To be normal, central limit theorem states that any one of the following must hold:
1. population distribution is normal
2. sampling distribution is symmetric, unimodal without outliers, and samples
size is less than or equal to 15
3. sampling distribution is skewed, unimodal, with outliers, and sample size is
between 16 and 40
4. sample size is greater than 40, with outliers
If one of the above is satisfied (must state which one is satisfied on the AP) then the critical value can
be expressed as a t-score or a z-score
To find t*, use the -t-distribution table(table B). Go to the row for your degrees of freedom (df) … that
is n – 1. Now, move to the column for your desired confidence level C – those numbers are at the
bottom. The intersection of the correct row and column is your t*. Note that if n is above 30, the
rows skip 10. It won’t matter much whether you use the lower or upper row as these values are
very close.
The value z* is a value found at the bottom of table B. If sample is large use ∞ .
The typical values for z* are: 90%: 1.645 95%: 1.96 99%: 2.576
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