HW #5 POL 251- Nov 9

Noah Leingang Dawson Jacks Destiny Carter POL 251: Introduction to Political Science Research Methods Homework #5 Question 1: A researcher obtains measurements of individuals’ egalitarian beliefs on a large random sample of U.S. adults. Each individual is measured along an egalitarianism scale that runs from a raw score of 0 (low egalitarianism) to a raw score of 24 (high egalitarianism). The mean of these respondents’ egalitarian values is 14, with a standard deviation of 5 – assume these respondents are the full population. 1. Obtain Z scores for the following egalitarianism scores (these scores are data points or x). For each, use the formula to calculate Z scores above, and show all of your work. a. 5 b. 9 c. 20 Answer : a. z= (5-14)/5 = -1.8 b. z= (9-14)/5= -1 c. z= (20-14)/5= 1.2 2. For each of the z scores you calculated above find the associated percentage of cases that falls to the left (or less than) the observed z-score. a. Your calculated z-score for 5 is 3.59% or .0359 b. Your calculated z-score for 9 is 15.87% or .1587 c. Your calculated z-score for 20 is 88.49% or .8849 Question 2: Imagine you are playing a game with a 20-sided die (d20). In this game, any roll of the die that is

15 or higher is considered a success – in other words rolling a 15, 16, 17, 18, 19, or 20 is considered a success. Any roll of 1 is considered a critical failure. 1. Are the outcomes in this game independent or mutually exclusive? Briefly explain your answer. The two outcomes, success and critical failure, are mutually exclusive because success and critical failure cannot happen together or simultaneously. 2. What is the probability of success in one game? Show all work. The probability of success in one game is 6/20, or 3/10. 30% probability. 3. What is the probability that a player will have success four turns in a row (i.e. What is Pr(Success) in 4 consecutive turns)? Please use proper notation for probabilities and show all work. Work: (6/20) 4 = 0.0081. This means that there is a 0.81% probability of this happening. 4. What is the probability that a player will have success in one turn, then a critical failure in the next turn? Please use proper notation for probabilities and show all work. Answer: P(Success) + P(critical failure)= P(A) + P(B) 30% + 5%= 35% Question 3: Imagine that N=50 POL 251 students were asked their opinions on learning statistics. Opinions were measured on a scale from 1 (hated learning statistics) to 5 (loved learning statistics). The mean is 3.5, and the standard deviation is .65. Note that this is the full population of POL 251 students. 1. Use the appropriate normal distribution (Z) lookup table to find the critical value with 𝛼 =0.05 and a two-tailed test. Write down that critical value and show your work if appropriate. Answer: Since this is a two-tailed test, must be divided by 2, according to Oct 31 ppt, slide 7 ? 0.05 / 2 = 0.025 Therefore the Z score is -1.96 2. Calculate the standard error of statistics opinions in this sample. Use scrap paper to show your work, and round answers to two decimal places. (Hint: SE = / ) √ √ √ √ √ √ √ √ √ √ √ √ √ √ √ Answer: .65 / √50 = 0.09 3. Calculate the 95% confidence interval of statistics opinions in this sample. Use scrap paper to show your work, and round answers to two decimal places. (Hint: C.I.=µ+/-Z*SE for the standard normal distribution). Answer: CI= 3.5 +/- (-1.96 * 0.09)