1. Lesson 5: Section 10.2 (part 2)
Comparing Two Means
Lesson 5: Section 10.2 (part 2)

2. objectives
Lesson 5:
Check conditions for using two-sample t procedures in a randomized experiment
Interpret the results of inference procedures in a randomized experiment
Determine the proper inference procedure to use in a given setting.

3. A few more things about two-sample t procedures
The Normal Condition : Remember that if your sample size is greater than 30, you assume the Normal condition is satisfied.
If it’s at least 15, then there should be no major skewness/outliers
If it’s less than 15, the graph of the data needs to appear roughly Normal
You do not need the same sample size from each population, but you do need to check the Normal condition for both.
If planning a two-sample study, choose equal sample sizes if you can (although not necessary).

4. Remember the calculator option “pooled”?
With a two sample t statistic, if the populations are Normal and the two populations have the same variance, it is possible to use a pooled two-sample t statistic.
It has more degrees of freedom n1 + n2 – 2, which gives us narrower confidence intervals and smaller P-values
This situation rarely happens in real life, so if you want larger degrees of freedom, use technology – do not use pooled!
If you are intrigued with this concept, page 645 gives a formula and description, but I suggest you do NOT use it.
This formula is on your formula sheet - CROSS IT OUT!
REMEMBER - WE DO USE POOLED TWO-SAMPLE Z TEST FOR A DIFFERENCE IN PROPORTIONS.
This is okay because the formula for standard error differs from the one we use with a two-sample test for a difference in means.

5. Inference for experiments
Remember, in experiments (like your paper planes project):
You need Randomization, Control, and Replication.
With the conditions of a two sample t interval/test:
Random: we do not sample at random from any larger populations, but we do randomize an order.
Normal: make sure your sample size is large enough or make a picture.
Independence: We assume that the specific treatment received doesn’t affect an individual subject’s response.

6. Two Sample t procedures VS. Paired data (one sample)
Use pair data (one sample t procedure) when: you are one subject receiving two treatments or you have matched pair designs (the express lane vs the regular lane example in Chapter 9)
Use two-sample t-procedures when: there are two independent groups of subjects.
The proper method depends on the design of the study!

7. EXAMPLE
Should you use paired data or two-sample t procedures to perform inference. Explain your choice.
A) To test the wear characteristics of two tire brands, A and B, one Brand A tire is mounted on one side of each car in the rear, while a Brand B tire is mounted on the other side. Which side gets which brand is determine by flipping a coin. The same procedure is used on the front.
B.) Can listening to music while working increase productivity? Twenty factor workers agree to take part in study to investigate this questions. Researchers randomly assign 10 workers to do a repetitive task while listening to music and the other 10 workers to do the task in silence.
Paired t procedures - matched pairs experiment
Two-sample t procedures – data are being produced using two independent groups of workers in a randomized experiment

8. homework Assigned reading: p. 627-651 HW problems: Lesson 3 – 5
Check answers to odd problems.