CONFIDENCE INTERVALS HONORS ADVANCED ALGEBRA PRESENTATION 1-9

VOCABULARY Confidence Interval – a range of values based on a sample that we can say the population mean will fall with a given % certainty. The correct mean will be captured in that % of sample intervals.

NECESSARY INFORMATION 1.A sample whose size is n ≥ 30 (preferred for our z- score calculation). 2.The mean of the sample. 3.The standard deviation of the population. 4.The confidence percentage that we want to calculate.

PROBLEM 1

PROBLEM 1 (CONT’D)

To find the standard deviation of the sample, we need to know the standard deviation of PSAT scores for the population. For the most recent test, it was about 33. Step 1: Calculate the standard deviation of the sample using the standard deviation that is given to us.

PROBLEM 1 (CONT’D) Now we want to decide how accurate we want to be. Using the Empirical rule of , we could estimate how accurate our interval was in including the actual population mean based on how many standard deviations we include. Step 2: Use the confidence interval you want to determine a margin of error. In this situation, let’s look for a 95% confidence interval.

PROBLEM 1 (CONT’D) Step 3: Use your sample mean and your margin of error to write an interval to your desired accuracy.

PROBLEM 1 (CONT’D)

PROBLEM 2 If we wanted an 80% confidence interval, what z-score would we use?

PROBLEM 3 If in our original problem, we wanted to improve our confidence to 99.7% without changing our interval, what sample size would we need?

HOMEWORK Worksheet on Confidence Intervals