STATS Exam 1 Study Guide Fall 2024 PDF

The first exam will cover material presented thus far in both the readings and in lecture. It will contain 32 multiple choice questions worth 2.5 points each (80 possible points) and problem set questions worth 20 points. A review session will be held during the class period before our exam. You ar...

The first exam will cover material presented thus far in both the readings and in lecture. It will contain 32 multiple choice questions worth 2.5 points each (80 possible points) and problem set questions worth 20 points. A review session will be held during the class period before our exam. You are encouraged to go over the study guide in order to be prepared with specific questions during the review session. The undergraduate TAs are also holding review sessions during their office hours (listed in the syllabus). They have practice problems from each chapter that you can work through with them. [Be sure to bring a **pen or pencil** , **your student ID,** and a **calculator** Approved for the ACT/SAT for the exam.] Below is the knowledge you're responsible for having for the exam: **\ [Chapter 1 -- Intro to Statistics:]** *Population vs Sample:* 1. Understand the concept of a population. 2. Understand the concept of a sample. 3. Understand the concept of a parameter. 4. Understand the concept of a statistic. *Categorization of variables (Discrete vs Continuous).* 5. Know how to define and identify discrete variables. 6. Know how to define and identify continuous variables. *Scales of variables (Nominal, Ordinal, Interval, Ratio)* 7. Know how to define and identify a nominal variable. 8. Know how to define and identify an ordinal variable. 9. Know how to define and identify an interval variable. 10. Know how to define and identify a ratio variable. *Experimental Design:* 11. Know how to define and identify a correlational study. 12. Know how to define and identify an experimental study. 13. Know how to define and identify a non-experimental study. 14. Know which types of studies have independent variables and dependent variables. 15. Know how to define and identify an independent variable. 16. Know how to define and identify a dependent variable. 17. Be able to identify different types of variables used in specific study (ie. discrete vs. continuous etc.) 18. Know which types of studies can identify causation. 19. Understand why studies that don't manipulate a variable cannot determine causality. **[Chapter 2 -- Frequency Distributions:]** *Frequency Tables* 1. Know the purpose of a frequency table. 2. Know how to read a frequency table. *Types of graphs* 3. Know how to interpret a bar graph. 4. Know how to interpret a histogram. 5. Know how to interpret a polygon. 6. Know when to use a bar graph, versus histogram/polygon, when given a dataset. 7. What characteristics define the Normal Curve. a. Why does the normal curve occur so often in natural phenomena? *Stem and Leaf Plots* 8. Know how to create a stem and leaf plot given a dataset. 9. Know how to read a stem and leaf plot and produce the dataset. 10. **[Chapter 3 - Central Tendency:]** *Descriptive Statistics* 1. When given a dataset, know how to compute: a. The mean. b. The median. c. The mode. 2. Know under what circumstances the mean does not provide a representative value. 3. In a symmetrical distribution what is the relationship between mean, median, and mode? *Shapes of Distributions:* 4. Know how to identify the different shapes of distribution graphs: d. Positive Skew. e. Negative Skew. f. Symmetrical. g. Bimodal 5. Know how to identify what type of distribution graph would occur based on a dataset. 6. Know how to identify what a potential dataset might look like given a distribution graph. 7. Understand why the normal curve occurs so often in real life data sets. **[Chapter 4 - Variability:]** 1. Know the notation "S" and "σ" 2. Know how to calculate the sum of squares given a dataset. 3. Know how to calculate the variance given a dataset. 4. Know how to find the standard deviation for both a sample and a population. a. Note: The formulas will be provided for you but will not labelled. b. Why do we use *df* as the denominator in the formula for s? 5. Know how to find the range (v1 and v2 from Chap 4: Slide 7). 6. Know why the range is an imprecise and unreliable measure of variability. 7. What is the most common measure of variability? 8. What does the standard deviation approximate (i.e. how do we interpret it)? 9. Know how to find the mean when given n (or N) and [\$\\sum\_{}\^{}x\$]{.math.inline} (without a dataset provided). 10. Know how to find the variance when given n (or N), [\$\\sum\_{}\^{}x\$]{.math.inline} and sum of squares (without a dataset). 11. Know how to find the standard deviation given n (or N) and the variance (without a dataset). 12. Be able to sketch an approximate smooth curve graph if given a mean and standard deviation. **[Chapter 5 - Z - Scores:]** 1. Know how to define a z-score. a. What does a z-score of 0 indicate? b. Are z-scores descriptive or inferential statistics? c. What is the advantage of using z-scores to compare populations? 2. Know how to calculate a z-score for a given value of X, if also given values for μ and σ. d. Ex. If *M* = 65 and σ = 10, what is the *z*-score for X = 70? 3. Know how to calculate the X value for a given *z*-score, if also given values for μ and σ. e. Ex. If *M* = 65 and σ = 10, what is the X value if *z* = 5? 4. Be able to draw a normal curve and indicate where a specified *z*-score would fall in relation to the *M*. 5. Know how z-scores are related to the standard deviation of a dataset. **\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\--** **PART II: PRACTICE PROBLEMS** [Multiple Choice Practice: (Correct answers are at the top of page 5)] For the following dataset: \[2, 2, 2, 3, 4.5, 1, 7, 3.5, 4, 3.5\] 1. Find the mean:  a) 3.25 b. 2  c. 2.5 d. 1.5 2. Find the median: a) 2 b. 1 c. 3 d. 3.25 3. Find the mode: a) 3.5 b. 2 c. 0.67 d. 1 4. The research design above is: A. Correlational B. Experimental C. Cross-sectional D. Non-experimental 5. In the research study from question \#4 (the one about Guinea Pigs on the previous page) what are the independent and dependent variables? A. Tooth length is the independent variable and Guinea Pig is the dependent variable. B. Tooth length is the independent variable and assignment to condition (Vitamin C vs. Water) the dependent variable. C. Guinea Pig is independent variable and tooth length is the dependent variable. D. Assignment to condition (Vitamin C vs. Water) is the independent variable and tooth length is the dependent variable. 6. Which distribution below shows the greatest negative skew? **~A\ B\ C\ D~**  *Correct answers to the multiple-choice practice problems are at top of next page.* [\ ]**Multiple Choice Answers: 1 = A; 2 = D; 3 = B; 4 = B; 5 = D; 6 = B;** [Problem Set Practice:] *Note: Be sure to show your work to allow the possibility of receiving partial credit on the practice problems.* *Take answers to two decimals places for final answers and to six decimals for any value you'll put into a formula to create another final answer. Round as needed. It's fine to drop the last decimal if it's a 0.* *Rounding examples: 24.50 = 24.5; 24.495 = 24.50 or 24.5; 24.49499999 = 24.49* **Problem \#1:** Assume the grades on the first PSYC 243 exam are roughly symmetric with μ = 80 and σ = 5 Your score on this test was an 87.5.   - What is the z-score for your test score? - Draw a normal curve and indicate where your score would land in relation to the mean. Your z-score on the test was *z* = -2 (*sorry!*). - What is the test score for your z-score? **Problem \#2:** Using the following data and the table below, fill in the X column appropriately and calculate (a) the *M* (3 pts), (b) the range (3 pts), (c) sample variance (3 pts), and (d) sample standard deviation (3 pts) and 3 pts for filling in table correctly (total 15 points) **Data: 2, 12, 8, 18, 0, 20** ------- --------- ------------- ------------------- **X** ***M*** **X - *M*** **(X -- *M*)^2^** ------- --------- ------------- ------------------- **Problem \#3:** In a class where the mean score (μ) on an exam is 70, a student achieved a score of 𝑋=62 X=62. Which of the following values for the standard deviation (σ) would result in the lowest percentile rank for this student? a. σ=6 b. 𝜎=9 c. 𝜎=12 Shown Work for Multiple Choice: For the following dataset: \[2, 2, 2, 3, 4.5, 1, 7, 3.5, 4, 3.5\] 1. **Find the mean: A. 3.25** 2. Problem Set Answers: **Problem \#1**: **z = +1.5** Problem \#1 Shown Work: **Test score = 70** 80 + (-2 x 5) = 70 **Problem \#2:** **Data: 2, 12, 8, 18, 0, 20** ------- --------- ------------- ------------------- **X** ***M*** **X - *M*** **(X -- *M*)^2^** 2 10 -8 64 12 10 2 4 8 10 -2 4 18 10 8 64 0 10 -10 100 20 10 10 100 ------- --------- ------------- ------------------- Problem \#2 Shown Work: a. (2+12+8+18+0+20) / 6 = 10 (sum of scores / \# of scores) b. 20 -- 0 = 20 (max score -- minimum score) c. (64 + 4 + 4 + 64 + 100 + 100) / (6-1) = 67.2 (average of squared deviations = sample variance) d. [\$\\sqrt{67.2} = 8.20\$]{.math.inline} (square root of sample variance) **Problem \#3:** Step1. Calculate the Z scores using this formula: \ [\$\$Z = \\frac{X - \\ \\mu}{\\sigma}\$\$]{.math.display}\ Step 2: Compare the Z scores for each standard deviation option provided: - For 𝜎=6, the Z-score would be: \ [\$\$Z = \\frac{62 - \\ 70}{6}\$\$]{.math.display}\ Z = -1.33 - For 𝜎=9, the Z-score would be: \ [\$\$Z = \\frac{62 - \\ 70}{9}\$\$]{.math.display}\ Z = -0.89 - For 𝜎=12, the Z-score would be: \ [\$\$Z = \\frac{62 - \\ 70}{9}\$\$]{.math.display}\ Z = -0.67 The lowest score is -1.33, the correct answer is 𝜎=6. These are the formulas you will be provided with for exam \#1. **Sum of Squares:** **Sum of Squares:** [∑]{.math.inline}(X - µ)^2^ [∑]{.math.inline}(X - *M*)^2^ **Variance:** **Variance:** [\$\\sigma\^{2} = \\ \\frac{\\sum\\left( X\\ - \\ \\mu \\right)\^{2}}{N}\$]{.math.inline} [\$s\^{2} = \\ \\frac{\\ \\sum\\left( X\\ - \\ M \\right)\^{2}}{n - 1}\$]{.math.inline} **Standard Deviation:** **Standard Deviation:** [\$\\sigma = \\sqrt{\\frac{\\sum\\left( X\\ - \\mu\\ \\right)\^{2}}{N}}\$]{.math.inline} [\$s = \\sqrt{\\frac{\\sum\\left( X\\ - \\ M \\right)\^{2}}{n - 1}}\$]{.math.inline} **z-Scores:** ***z*-Scores:** *z* = [\$\\ \\frac{X - \\mu}{\\sigma}\$]{.math.inline} *z* = [\$\\frac{X - M}{s}\$]{.math.inline} [*Χ*]{.math.inline} = [*μ*]{.math.inline} + z[*σ*]{.math.inline} [*Χ*]{.math.inline} = [ M]{.math.inline} + z[*s*]{.math.inline}