2 Sample Confidence intervals for proportions

1. 2 Sample Confidence intervals for proportions By Kaitlin, Bobbye, Dylan

2. What is a confidence interval? are the estimated plus or minus of some amount (ex: 50% - 2% to 50% + 2% OR 48% to 52%) The 2% from our example can be referred to as the Margin of Error this tells us how far from the population value our estimate can be • Confidence interval provides 2 pieces of info: • A range of possible values for our population parameter • An confidence interval expresses our level of confidence in this interval

3. When testing our confidence interval we want to have a higher confidence because we want to our information to be more accurate. (ex: 95%, 99% is very confident and will give us accurate info. Vs a confidence of 68%) • What the signs mean  • n1= sample size in sample 1 • n2= sample size in sample 2 • p^1= proportion of successes in sample 1 (p^1/n1) • p^2= proportion of successes in sample 2 (p^2/n2)

4. Problem example!!! A study by the National Athletic Trainers Association surveyed random samples of 1679 high school freshmen and 1366 high school seniors in Illinois. Results showed that 34 of the freshmen and 24 of the seniors had used anabolic steroids. Steroids, which are dangerous, are sometimes used to improve athletic performance. Does this data show that there is a significantly different proportion of freshmen using steroids than seniors using steroids. Carry out a 2-proportion hypothesis test at an alpha level of 0.05. • Null Hypothesis Ho: pfreshmen = pseniors • Alternative Hypothesis Ha: pfreshmen ≠ pseniors • (Where pfreshmenis the proportion of all high school freshmen who use steroids and pseniorsis the proportion of all seniors who use steroids.)

5. Open stat crunchclick stat proportion stats  two sample  with summaryThen….insert your # of successes and observations-click confidence interval and input your confidence -click compute (…back to our example…) Sample 1: # of successes=34 # of observations=1679 Sample 2: # of successes=24 # of observations=1366 • Confidence interval for p1 - p2 Level = 0.95 (95%) (***We used a confidence level of 95% because out alpha was at 5%**)

6. 95% confidence interval results:p1 : proportion of successes for population 1p2 : proportion of successes for population 2p1 - p2 : Difference in proportions ***REMEMBER  “Does this data show that there is a significantly different proportion of freshmen using steroids than seniors using steroids”*** “We are 95% confident that the interval from about -0.007011 to 0.012372 captures the true unknown population proportion of _________.”