susan wardak Per .. Date _5/5/2022 Confidence Interval for the Difference of 2 Means Here is a problem that you looked at in worksheet 9.3: "During the 2013-2014 season. De Andre Jordan of the L. A. Clippers led the league with 1114 rebounds in 82 games. His standard deviation was 4.000. Estimate his ABILITY to make rebounds per game" Once you recognize that this is solved by creating a confidence interval for a mean (rebounds divided by games), you apply the formula to get: 13.585 + .883 Formula for 95% confidence interval for a mean: or: from 12.702 to 14.468 We are 95% confident that the interval of plausible values from 12.702 to 14.468 X + 2 -S includes DeAndre Jordan's ABILITY to get rebounds in the 2013-2014 season. Now suppose you want to create a confidence interval for the difference between his ABILITY to get rebounds in home games and his ABILITY to get rebounds in away games. This would require a new type of confidence interval with a new (although familiar looking) formula: 95% Confidence Interval for the Difference of 2 Means: variables: formula for 95% confidence interval for the difference of 2 means: XA = observed mean value in context A (PERFORMANCE at home) X B = observed mean value in context B (PERFORMANCE away) ( X , - X. ) + 27 + SA = standard deviation in context A SB= standard deviation in context B NA = number of observations in context A B = number of observations in context B Here is the data for DeAndre Jordan for the 2013-2014 season. Use it to construct a 95% confidence interval for the difference between his ABILITY to get rebounds in home games and his ABILITY to get rebounds in away games: Home way ( X , - X . ) = 27 + n nB Rebounds 541 573 Games 41 41 Per game 13.195 13.976 SD 3.407 4.525P6 515/22 Practice exercise: ( 1 ) Many people believe that the NBA was more focused on offense in the 1980s and more focused on defense in the 1990s. How much greater was the ABILITY to score in the 1980s compared to the 1990s for NBA teams? Here are some summary statistics and graphs to compare these distributions. POINTS PER GAME 1995 Mean 110.8 101.4 1095 1965 Standard deviation 4.45 5.03 Number of teams 23 27 90 05 100 105 110 115 120 Points per game ( a ) Calculate a 95% confidence interval for the difference in the ABILITY to score for NBA teams in 1985 and 1995. ( X - X. ) + 21/ SA + n ( b ) Interpret the confidence interval in context. ( c ) Does the interval provide convincing evidence that NBA teams had a greater ABILITY to score in 1985 than in 1995? Explain