1. Lecture 8 Dustin Lueker

2.  Two independent samples ◦ Different subjects in the different samples ◦ Two subpopulations  Ex: Male/Female ◦ The two samples constitute independent samples from two subpopulations  Two dependent samples ◦ Natural matching between an observation in one sample and an observation in the other sample  Ex: Two measurements of the same subject  Left/right hand  Performance before/after training ◦ Important: Data sets with dependent samples require different statistical methods than data sets with independent samples 2STA 291 Winter 09/10 Lecture 8

3.  Take independent samples from both groups  Sample sizes are denoted by n 1 and n 2 ◦ To use the large sample approach both samples should be greater than 30  Subscript notation is same for sample means 3STA 291 Winter 09/10 Lecture 8

4.  In the 1982 General Social Survey, 350 subjects reported the time spend every day watching television. The sample yielded a mean of 4.1 and a standard deviation of 3.3.  In the 1994 survey, 1965 subjects yielded a sample mean of 2.8 hours with a standard deviation of 2. ◦ Construct a 95% confidence interval for the difference between the means in 1982 and 1994.  Is it plausible that the mean was the same in both years? 4STA 291 Winter 09/10 Lecture 8

5.  For large samples ◦ For this we will consider a large sample to be those with at least five observations for each choice (success, failure)  All we will deal with in this class  Large sample confidence interval for p 1 -p 2 5STA 291 Winter 09/10 Lecture 8

6.  Is the proportion who favor national health insurance different for Democrats and Republicans? ◦ Democrats and Republicans would be your two samples ◦ Yes and No would be your responses, how you’d find your proportions  Is the proportion of people who experience pain different for the two treatment groups? ◦ Those taking the drug and placebo would be your two samples  Could also have them take different drugs ◦ No pain or pain would be your responses, how you’d find your proportions 6STA 291 Winter 09/10 Lecture 8

7.  Two year Italian study on the effect of condoms on the spread of HIV ◦ Heterosexual couples where one partner was infected with HIV virus  171 couples who always used condoms, 3 partners became infected with HIV  55 couples who did not always use a condom, 8 partners became infected with HIV ◦ Estimate the infection rates for the two groups ◦ Construct a 95% confidence interval to compare them  What can you conclude about the effect of condom use on being infected with HIV from the confidence interval?  Was your Sex Ed teacher lying to you? 7STA 291 Winter 09/10 Lecture 8

8. 8  To calculate the confidence interval, we use the Central Limit Theorem (np and nq ≥ 5) ◦ What if this isn’t satisfied?  Instead of the typical estimator, we will use  Then the formula for confidence interval becomes STA 291 Winter 09/10 Lecture 8

9.  Suppose a student in an advertising class is studying the impact of ads placed during the Super Bowl, and wants to know what the proportion of students on campus watched it. She takes a random sample of 25 students and finds that all 25 watched the Super Bowl. ◦ Find a 95% confidence interval using first method learned for p ◦ Find a 95% confidence interval using the new method if np, nq condition fails STA 291 Winter 09/10 Lecture 89