The following is a made-up data set that contains scores for 10 children. Data are parents' ratings of children's empathy. Empathy was rated on a scale of 1 (exhibits no empathy for others) to 10 (exhibits extremely high empathy for others). Subject ID number Empathy 1 3 2 2 3 6 4 3 5 5 6 6 7 2 8 8 9 3 10 6 1. Using the data set above, compute the sample mean for Empathy ( ). For full credit, be sure to show all of your work. (1 point .5 point for correct answer and .5 point for showing work) 2. Let's assume that the population mean of children's empathy is = 6 and the population standard deviation is = 2. We want to know whether our sample mean of empathy (the mean computed above) came from the population of children's empathy. In other words, we want to know if our sample mean is equal to the population mean. To determine this, we need to do a one-sample z test. Please compute a one-sample z test by hand using the information from question 1 (sample mean [ ], sample size [N]) and the information given here (population mean [] and population standard deviation []). Report your answer for the sample statistic Zobs using three decimal places (thousandths). For full credit, be sure to show all of your work. (2 points 1 point for correct answer, 1 point for showing all work) Formulas: Z obs = **3. Let's say we state the hypotheses that Ho: = and H: . Note that this is a non-directional research hypothesis. We have set our significance level at a = .05. We determine that we should compute a one-sample z test. We already have computed the test statistic for the z test. What are the boundary values needed to reject the null hypothesis (specify the sign[s] of the values)? For full credit, be sure to show all of your work. (2 point - 1 point for correct answer and 1 point for showing work) 4. Using the information from questions 2 and 3, what is the conclusion from the one-sample z test? Do we reject the null hypothesis or do we fail to reject the null hypothesis? (1 point for correct answer) 5. The mean Verbal SAT score for the population of first-year students at ASU is 520. The standard deviation of scores in this population is 95. An investigator believes that the mean Verbal SAT of first-year psychology majors is significantly different from the mean score of the population. The mean of a sample of 25 first-year psychology majors is 548. Please test the investigator's prediction using an alpha level of .05. Show your work. (4 points - 3 points for correct answer. 1 point for showing work)