Statistical Analysis – Chapter 8 “Confidence Intervals” Roderick Graham Fashion Institute of Technology

The Logic Behind Confidence Intervals An Example  What if we wanted to know the creativity of FIT students, but as researchers, we are the first to take these measurements. We are not testing hypotheses and we have no population value to compare to our sample. What do we do in this case?  In this situation, our sample mean,,that we calculate is the “best guess” or “best estimate” of the population. Our sample of FIT students will represent all FIT students.

The Logic Behind Confidence Intervals  Although the sample mean that we calculate is a good estimate, we know that our sample is affected by randomness (Maybe there are a few very creative students in our sample that skew the numbers).  Therefore, we want to construct a confidence interval that will allow us to say, conceptually: “although I cannot be sure that my calculated mean is the true value of the population, I can be sure with 99% confidence that the REAL population value is between ___ and ____.”

The Logic Behind Confidence Intervals  Before the election in 2008, most experts had a good idea who would win each state.  This is because a point estimate was done on small sample of likely voters. Let’s see an example:

What Equations Do We Use? The z c ’s and t c ’s are associated with levels of probability on the normal curve table. z. 95 = a z-score of 1.96 t. 95 = a t-score, for df of 5, of 2.57 s = standard deviation, and n = the number of cases, or respondents

T-Table for Confidence Intervals Look for your desired confidence interval Find your df (degrees of freedom). Remember, this is n – 1.

Calculating Confidence Intervals Step 1 – Choosing a Confidence Level  This is only a matter of choosing a z-score or t-score  These scores are symbolized as Z c or T c  For sample sizes with an N under 30, you would use a t- score  Question: Why can I not construct a similar table for t- scores? Z Scores for Common Confidence Intervals Z – Score (30 or more) 90% % %2.58

Calculating Confidence Intervals Step 2  Calculate E using these equations…  This E is called “the maximum error of estimate”

Calculating Confidence Intervals Step 3  Solve for the confidence interval using this equation: The x-bars are the means from the sample. The E’s are the maximum error of estimate you calculated with the prior equation You do not calculate µ, this is the population value you cannot know

Sample Problem – 8.6

8.6 (A)

8.6 (B and C)

Sample Problems – 8.4

Question 8.4

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