EstimatingPopulation Parameters

andMargins of Error

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)

How to compute the margin of Error

• Given population attributes and the standard deviation of the statisticME= Critical Value x Standard Deviation of Statistic

• Given sample attributes and know the standard error of the statisticME= 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)

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 normal2. sampling distribution is symmetric, unimodal without outliers, and samples size is less than or equal to 153. sampling distribution is skewed, unimodal, with outliers, and sample size is between 16 and 404. 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