1. Assume I have a dataset that represents a population of Xvalues (mean = 4; standard deviation = 1.58). Calculate z-scores for Xvalues = 2.5, 6.2, and 9.0. Interpret these results (one sentence per z-score). (6 points)

1. A dean must distribute salary raises to her faculty for next year. She has decided that the mean raise is to be $2000, the standard deviation of raises is to be $400, and the distribution is to be normal. She will attempt to distribute these raises based on merit, meaning that people whose performance is better will get higher raises.

1. The most productive 10% of the faculty will have a raise equal to or greater than $___. (3 points)
2. The bottom 5% of the faculty will receive no more than $ ___ each. (3 points)

1. Suppose I gave an exam, and the average grade in the class on that exam was a 78, with a standard deviation of 4. What raw exam score is the 90th percentile in this class? (Remember: "90th percentile" means "scores higher than 90% of the other scores in the sample.")(4 points).

1. On a different exam, the class average was a 195 with an SD of 30. What two values of X (raw exam scores) would encompass the middle 50% of scores? (Hint: See mynormal distribution and z-scores.R file.)(4 points).

1. Imagine I've conducted a study to examine the correlation between trait optimism and relationship satisfaction. I analyze my data and find that these two variables are correlated at r= .45. (14 points)

1. What type of correlation did I run? (In other words, what does the rsymbol mean?)
2. What type of data are my two variables (nominal, ordinal, interval, or ratio)?
3. What is the direction of this correlation?
4. How would you interpret the magnitude of this correlation?
5. As relationship satisfaction scores decrease,what is happening to trait optimism scores?
6. Why can I NOT say that trait optimism and relationship satisfaction are causally related? Give at least two reasons.
7. If I created a scatterplot of this correlation, what would the regression line/line of best fit look like?

1. Imagine I conduct a study in which I test the effectiveness of music listening on running speed. One group of participants listens to a song of my choosing while they run, and another group of participants listens to no music while they run. (4 points)
   1. What is my independent variable?
   2. What is my dependent variable?
   3. What kind of statistical analysis would I use to determine the difference in running speed between these two groups?
   4. What is the null hypothesis in this scenario?