1. SWBAT: -Interpret the t-distribution and use a t- distribution table -Construct a confidence interval when n<30, the population is normally distributed, and σ is unknown. Agenda: -Review homework -Notes: power point -Assign Homework

2. Confidence Intervals for Mean (Small) - a t-distribution is used when the following occur: population is approximately normal the sample size is less than 30 the population standard deviation is unknown A t-distribution: -Is bell shaped and symmetrical about the mean -Has an area under the curve is 100% -Uses the degree of freedom which is equal to n – 1 -As the degree of freedom approaches 30 the graph will begin to resemble a normal distribution (z distribution)

3. Normal Distribution n ≥ 30 T Distribution n < 30

4. Reading a t distribution table: 1.Determine the Degree of Freedom (down left side of table) 2.Determine if you are doing a confidence interval, one tail, or two tail test to determine the correct column Example: Find the critical t score for a sample size of 25 with a confidence level of 90% d.f. = 24 t c score = ±1.711 Example: Find the critical t score for a sample size of 8 with a confidence level of 98% d.f. = 7 t c score = ±2.998

6. Example: A random sample of 20 acres gave a mean yield of wheat equal to 41.2 bushels per acre with a standard deviation of 3 bushels. Assuming that the yield of wheat per acre is normally distributed, construct a 90% confidence interval for the population mean µ.

7. Normal Distribution vs t Distribution Is sample 30 or more? If yes, then use Normal Distribution If no, is the population approximately normally distributed? If yes, do you know population standard deviation? If no, cannot use normal or t distribution If yes, then use normal distribution If no, then use t distribution

8. Example: You randomly select 20 Brooke Point students that work a part time job and ask them how much they earn a week. The sample mean is $172.37 with a sample standard deviation of $13.05. Assuming the distribution of wages is normally distributed, should you use normal distribution, t distribution or neither to construct a 99% confidence interval for the population mean? Explain your reasoning. - Sample is less than 30 - Population is normally distributed - Know sample standard deviation, not the population standard deviation Therefore, use t distribution

9. Homework Pg 323 # 10-30 even