1. Statistics: Unlocking the Power of Data Lock 5 Section 6.11 Confidence Interval for a Difference in Means

2. Statistics: Unlocking the Power of Data Lock 5 Outline Confidence interval for a difference in means

3. Statistics: Unlocking the Power of Data Lock 5

4. Confidence Interval The general formula for a confidence interval is statistic  z*  SE For means, replacing  with s causes us to use the t-distribution instead of the standard normal For means: statistic  t*  SE

5. Statistics: Unlocking the Power of Data Lock 5 statistic  t*  SE Degrees of freedom for the t-distribution is the smaller of n 1 – 1 and n 2 – 1

6. Statistics: Unlocking the Power of Data Lock 5 Video Games and GPA 210 first-year college students were randomly assigned roommates For the 78 students assigned to roommates who brought a videogame to college: average GPA after the first semester was 2.84, with a sd of 0.669. For the 132 students assigned to roommates who did not bring a videogame to college, average GPA after the first semester was 3.105, with a sd of 0.625. How much does getting assigned a roommate who brings a videogame to college affect your first semester GPA? Give a 90% CI.

7. Statistics: Unlocking the Power of Data Lock 5 Videogames and GPA We are 90% confident that getting assigned a roommate who brings a videogame to college decreases the mean first semester GPA by between 0.11 to 0.42 points. 1. Check conditions: 4. Calculate standard error: 5. Calculate CI: 5. Interpret in context: 78 ≥ 30, 132 ≥ 30 2. Find t*: t with 78 – 1 = 77 df, 90% CI: => t* = 1.665 3. Calculate statistic:

8. Statistics: Unlocking the Power of Data Lock 5 Video Games and GPA statistic  t*  SE (-0.42, -0.11) We are 90% confident that getting assigned a roommate who brings a videogame to college decreases the mean first semester GPA by between 0.11 to 0.42 points. t* = 1.665 df = smaller of 78 -1 = 77 and 132 – 1 = 131, so df = 77