STATISTICS 141 Final Review

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1 STATISTICS 141 Final Review Bin Zou Department of Mathematical & Statistical Sciences University of Alberta Winter 2015 Bin Zou STAT 141 Final Review Winter / 20

2 Information Date: April 17, 2015 (Friday) Time: 14:00-17:00 (3 hours) Location: Main Gymnasium (Butterdom) Rows 13, 15, 17, 19, 21, 23 (Seats 1-15) There are 50 multiple choice questions. Each question has one and only one correct answer. You are supposed to answer ALL questions. This is a closed book exam. You will be given with a formula sheet and z-table. You need to mark all your answers on the Scantron sheet. Please bring your own calculator. Please read Final Information on eclass. Bin Zou (bzou@ualberta.ca) STAT 141 Final Review Winter / 20

3 Part I Ch.1 - Ch. 18 (excl. Ch.17) Approximately 20% (around 10 Questions) Bin Zou (bzou@ualberta.ca) STAT 141 Final Review Winter / 20

4 Descriptive Statistics (2-3 Q) Ch.1 You may skip. Ch.2 Distinguish Categorical and Quantitative Variables. Ch.3 Read Bar charts and Pie charts. Ch.4 Important! 1 Calculate mean and standard deviation (variance) from raw data. 2 Find Q1, Q2, Q3, or in general percentile from raw data. 3 Range = Max - Min; IQR= Q3 - Q1. 4 Lower fence = Q1-1.5 IQR; Upper fence = Q IQR; know how to find outliers. 5 Describe the shape of a distribution! Identify skewed to the left/right! Ch.5 Read boxplots: centre and spread. Bin Zou (bzou@ualberta.ca) STAT 141 Final Review Winter / 20

5 (PF2 Q30) The lifetimes (in thousands of hours) of sixteen electronic devices of the same model are as follows: Find the 5-number summary of this dataset. (PF1 Q1) There are many questions regarding Descriptive Statistics on midterm. Please try to solve those questions (posted on eclass). Bin Zou STAT 141 Final Review Winter / 20

6 Ch.6 Normal Modal Usually, no question is directly asked from Ch.6 on final. But contents in Ch.6 is very important! You MUST know how to use z-table: 1 find probability given z-value e.g., find P(z < 1.25), P( 1.96 < z < 1.65), P(z > 0.88). 2 find z-table given probability e.g., P(z <?) = 10%, P(? < z <?) = 60%, P(z >?) = 5%. You MUST be able to do standardization: PF2 Q37 X N(µ,σ) z = X µ σ. Bin Zou (bzou@ualberta.ca) STAT 141 Final Review Winter / 20

7 Ch.7-9 Regression Modal (3+ Q) 1 Find the regression line: ŷ = b 0 + b 1 x. 2 Predict y based on the regression model and calculate residual, y ŷ (true - predicted). 3 Explain the meaning of b 0 (intercept) and b 1 (slope). 4 Properties about r (refer to lecture notes). 5 R 2 = r 2 : measures the proportion of variation in y that can be explained by the regression model. PF1 Q2, Q3 PF2 Q20, Q21, Q48 Bin Zou (bzou@ualberta.ca) STAT 141 Final Review Winter / 20

8 Ch Gathering Data (1-2 Q) Types of Sampling 1 Simple random sampling: randomly select individuals from the population. 2 Stratified sampling: divide the population into groups, and randomly select from each group. 3 Cluster sampling: divide into clusters, and randomly select from some clusters. 4 Systematic sampling: pick based on some rules. 5 Voluntary sampling: individuals participate at their own willingness. Types of study 1 Observation. 2 Experiment. 3 Retrospective study vs Prospective study. Example: PM1 Q1, Q2; PM2 Q13, Q14. Bin Zou (bzou@ualberta.ca) STAT 141 Final Review Winter / 20

9 Ch Probability (4-5 Q) 1 Set operations: A C, A B, A B. 2 Addition rule: P(A B) = P(A) + P(B) P(A B). P(A B) 3 Conditional probability: P(A B) =. P(B) 4 Independent sets: P(A B) = P(A) P(B). (alternative rules?) 5 Disjoint sets: P(A B) = 0. 6 Construct a probability model from given information. 7 Calculate µ and σ from a probability model. 8 Calculate µ and σ by formula, PF1 Q5, Q7; PF2 Q10, Q38 E(aX + by + c) = ae(x) + b E(Y ) + c; Var(aX + by + c) = a 2 Var(X) + b 2 Var(Y ). Bin Zou (bzou@ualberta.ca) STAT 141 Final Review Winter / 20

10 Ch.18 Sampling Distribution (1-2 Q) 1 Sampling proportion 2 Sampling mean ˆp N ( p, ( ȳ N µ, ) pq n ) σ n PF1 Q9; PF3 Q37 Bin Zou (bzou@ualberta.ca) STAT 141 Final Review Winter / 20

11 Part II Ch.19 - Ch. 28 (excl. Ch.27) Approximately 80% (around 40 Questions) Bin Zou (bzou@ualberta.ca) STAT 141 Final Review Winter / 20

12 Constructing Confidence Interval (5+ Q) General formula: Estimate ± Critical Value S.E. 1 One-sample proportion p. PF1 Q10 2 Two-sample proportion difference p 1 p 2. PF1 Q17 3 One-sample mean µ. PF1 Q14 4 Two-sample mean difference µ 1 µ 2 : pooled; non-pooled; paired. PF1 Q28, Q30 Remark: In proportion questions (both one-sample and two-sample), S.E. have different formulas for C.I. and test. Bin Zou (bzou@ualberta.ca) STAT 141 Final Review Winter / 20

13 Understanding Confidence Interval (3+ Q) 1 You need to know how to interpret a C.I., We are 95% confident that... Most likely, 1 Q on one-sample and 1 Q on two-sample. PF1 Q18, Q31 2 Use a given C.I. to make conclusions for a test. Check whether the value being tested is included in the C.I. or not. If yes, fail to reject H 0 ; if not, then reject H 0. I expect at least 1 Q on two-sample either proportion or mean (check 0). PF1 Q20 Bin Zou (bzou@ualberta.ca) STAT 141 Final Review Winter / 20

14 Sample Size (2 Q) Sample size for desired margin of error: 1 For one-sample proportion, (PF1 Q11) ( ) CV 2 n = p(1 p). ME 2 For one-sample mean, (PF1 Q24) ( ) CV 2 n = ( ˆσ) 2. ME ME (margin of error) will be given by the question. (keyword: within, less than,...) CV is obtained from z-table under certain confidence level (90%, 95%, etc). If p is not given, then take p = 0.5. Remember to round up to the nearest integer for n. Bin Zou (bzou@ualberta.ca) STAT 141 Final Review Winter / 20

15 Type I and Type II Error (1 Q) 1 Type I error: we reject H 0, but in fact H 0 is true. Probability of making type I error is no more than α (Why?) 2 Type II error: we fail to reject H 0, but in fact H 0 is false. PF1 Q15; PF2 Q34 Bin Zou (bzou@ualberta.ca) STAT 141 Final Review Winter / 20

16 P-Value (2+ Q) 1 Interpreting P-value, PF1Q16. Remark: P-Value is a conditional probability given H 0 is true. 2 Find P-value using t-table. Determine df, and then compare the t-value with critical values. PF1 Q21 3 Compare P-value with α to make conclusions for an inferential test. Bin Zou (bzou@ualberta.ca) STAT 141 Final Review Winter / 20

17 Hypotheses (4+ Q) 1 (p problem) H 0 : p = p 0 H a : three options (>, <, ). PF1 Q12 2 (p 1 p 2 problem) H 0 : p 1 p 2 = 0. PF2 Q40 3 (µ problem) H 0 : µ = µ 0. PF1 Q22 4 (µ 1 µ 2 problem) H 0 : µ 1 µ 2 = 0. PF1 Q26 5 (ANOVA) H 0 : µ 1 = µ 2 = = µ k H a : NOT all means are equal. Wrong! All means are NOT equal. PF1 Q40 6 (Chi-square goodness-of-fit) H 0 : actual observations fit with the expected distribution. PF1 Q37 7 (Chi-square homogeneity) H 0 : homogeneous (no difference) H a : non-homogeneous/different 8 (Chi-square independence) H 0 : two categorical variables are independent. H a : two categorical variables are NOT independent. Bin Zou (bzou@ualberta.ca) STAT 141 Final Review Winter / 20

18 Performing Tests 1 One-sample z-test (one proportion p): 1 Q. PF1 Q12 2 Two-sample z-test (difference p 1 p 2 ): 1+ Q. PF1 Q19 3 One-sample t-test (one mean µ): 1 Q. PF1 Q23 4 Two-sample pooled t-test (µ 1 µ 2 ): 1+ Q. PF1 Q26 5 Two-sample non-pooled t-test (µ 1 µ 2 ): 1+ Q. PF1 Q29 6 Paired t-test (µ 1 µ 2 ): 1+ Q. PF1 Q25 Bin Zou (bzou@ualberta.ca) STAT 141 Final Review Winter / 20

19 ANOVA (4 Q) 1 Hypotheses: 1 Q. PF1 Q40 2 Degrees of freedoms: 1 Q. PF1 Q41 3 Calculate MS, SS, and eventually, F-ratio: 1 Q. PF Other topics: conditions (equal variance PF1 Q43; making conclusions (PF2 Q17); Bin Zou (bzou@ualberta.ca) STAT 141 Final Review Winter / 20

20 Chi-square Test (4 Q) 1 1+ Q on hypotheses, likely for a goodness-of-fit test. PF1 Q Q on choosing the right test: goodness-of-fit; homogeneity; independence. PF1 Q34 3 Calculate χ 2 for a goodness-of-fit test. PF1 Q38 4 Calculate expected count or contribution towards χ 2 for a cell in a homogeneity/independece test. PF1 Q35 Bin Zou (bzou@ualberta.ca) STAT 141 Final Review Winter / 20