Chapter 14 - Confidence Intervals: The Basics Confidence Interval = estimate + margin of error Purpose is to estimate an unknown population parameter and give some indication of how accurate the estimate is. ex: Test Scores: (0-500), n=840 people What is the mean for this test in the population? According to the 68-95-99.7 Rule, 95% of all samples should have a mean that falls within 2 std. devs. (s) of the population mean 272 is our estimate of the population mean…

2s = 2(2.1) = 4.2 So 95% of all samples should have a mean somewhere between 272 + 4.2 We call this a “95% Confidence Interval” 272 + 4.2 margin of error estimate

“Level C” Confidence Interval C = decimal form of confidence percentage ex: 95% conf. int. --> C = .95 Definition: An interval computed from sample data by a method that has probability “C” of producing an interval containing the true value of the parameter.” z* = unknown number of standard deviations to produce a given confidence interval. ex: Find z* for an 80% confidence interval.

Need a z-value with .9 to its left… 80% 90% Need a z-value with .9 to its left… 10%

Calculator Steps Select STAT--TESTS--#7 Set to the following values:

Interval Formula ex: Blood sample drug concentration Find a 99% confidence interval… Z* = 2.576

Interval =

Confidence Interval Behavior Margin of Error (m) = Changing any of the values in the equation will change the margin of error… The margin of error will decrease when: z* gets smaller  gets smaller n gets larger (4n to reduce m by half…) ex 14.4, pg 361

= 7.1 Choosing the sample size The confidence interval for a population mean will have a specified margin of error (m) when the sample size is: ex: Blood sample drug concentration Produce results accurate to within +0.005 with 95% confidence… how many measurements will we need to average? m = .005 z* = 1.96 for C=.95 =.0068 = 7.1 ** n generally will need to be whole numbers - so we must take 8 measurements…