Inference for the Mean of a Population Section 11.1 AP Exam Registration Deadline: March 17 th Late Fee ($50): March 18 th – March 24 th Financial Aid Application Due: TODAY!!!!!! Get out homework!

Conditions for Inference about a Mean  SRS of size n from the population of interest  Observations must be independent  Observations must have a normal distribution with mean µ and standard deviation σ

What if σ isn’t given?  Because σ is usually unknown, we estimate it by the sample deviation s.

Standard Error

The t distribution

Different t distributions?  There is a different t distribution for each sample size.

So how do we determine which one we use?  Degrees of freedom n -1, where n is the sample size.

Example 11.1, p. 619 Using the “ t Table” What critical value t * from Table C (t Table) would you use for a t distribution with 18 degrees of freedom having probability 0.90 to the left of t * ?

Example 11.1, p. 619 Using the “ t Table” What critical value t * from Table C (t Table) would you use for a t distribution with 18 degrees of freedom having probability 0.90 to the left of t * ? Before we start, we will need the tail probability..90 probability Tail area =.10

Df = 18, Tail Area =.10

Example 11.1, p. 619 Using the “ t Table” What critical value t * from Table C (t Table) would you use for a t distribution with 18 degrees of freedom having probability 0.90 to the left of t * ? So the desired critical value is t * =

Example 11.1, p. 619 Using the “ t Table” Now suppose you want to construct a 95% confidence interval for the mean µ of a population based on an SRS of size n = 12. What critical value of t * should you use? Df = 12 – 1 = 11 Tail Area? We don’t need it…look at the bottom of the chart.

Example 11.1, p. 619 Using the “ t Table” Now suppose you want to construct a 95% confidence interval for the mean µ of a population based on an SRS of size n = 12. What critical value of t * should you use?

Example 11.1, p. 619 Using the “ t Table” Now suppose you want to construct a 95% confidence interval for the mean µ of a population based on an SRS of size n = 12. What critical value of t * should you use? So the desired critical value is t * =

Homework:  P. 619: 11.1 a, 11.2, 11.4 Due: Tuesday FYI: I have a meeting Friday morning, 3/8. I will have to cancel tutoring that day.