Difference in Proportions

We’re trying out 4 different sugar cookie products. The following intervals are the result of a 95% confidence interval of likeability. Do the intervals provide convincing evidence? Product A: 0.05 to 3.1 Product B: 0 to 4.2 Product C: to 0.02 Product D: -2.3 to -2.0 Ye s No

 H 0 : Hamilton has the same ABILITY to get a hit at home and on the road in the 2010 regular season. H a : Hamilton has a greater ABILITY to get at home than on the road in the 2010 regular season.  Test statistic = BA home - BA away = 103/264 – 83/254 = – = Hamilton’s batting average is estimated to be greater at home than on the road.

 Simulation gives a p-value of 0.15 There is a 15% chance that Hamilton’s difference in BA will be at least by RANDOM CHANCE.  We do not have convincing evidence that Hamilton’s ABILITY to get a hit at home was better than on the road.

Hypothesis Test OR Confidence Interval

Confidence Interval = center ± margin of error Where P = PERFORMANCE n = # of attempts

Remember, BA home = 103/264=0.390 & BA away =83/254=0.327 Confidence Interval Margin of Error Standard Deviation

We are 95% confident the interval of plausible values from to includes the difference in Hamilton’s ABILITY to get a hit at home and on the road.

 positive possibilities, then the athlete's ABILITY is better in context 1 than context 2. a a 0, then the athlete's ABILITY is the same in both contexts.  negative possibilities, then the athlete's ABILITY is worse in context 1 than context 2.

(Hamilton’s difference in BA interval is from to ) We do not have convincing evidence that Hamilton’s ABILITY to get a hit at home was better than getting a hit on the road.

 If we want to estimate the difference in an athlete's ABILITY in two contexts, we can calculate a confidence interval for a difference in proportions (if the data are categorical).  We can decrease the margin of error in a CI by:  increasing the sample size  decreasing the number of standard deviations (AKA the multiplier)