STATISTICS 141 Final Review Bin Zou bzou@ualberta.ca Department of Mathematical & Statistical Sciences University of Alberta Winter 2015 Bin Zou (bzou@ualberta.ca) STAT 141 Final Review Winter 2015 1 / 20
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 2015 2 / 20
Part I Ch.1 - Ch. 18 (excl. Ch.17) Approximately 20% (around 10 Questions) Bin Zou (bzou@ualberta.ca) STAT 141 Final Review Winter 2015 3 / 20
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 = Q3 + 1.5 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 2015 4 / 20
(PF2 Q30) The lifetimes (in thousands of hours) of sixteen electronic devices of the same model are as follows: 68 82 83 83 86 86 87 87 89 91 92 93 96 100 106 108 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 (bzou@ualberta.ca) STAT 141 Final Review Winter 2015 5 / 20
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 2015 6 / 20
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 2015 7 / 20
Ch.11-13 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 2015 8 / 20
Ch.14-16 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 2015 9 / 20
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 2015 10 / 20
Part II Ch.19 - Ch. 28 (excl. Ch.27) Approximately 80% (around 40 Questions) Bin Zou (bzou@ualberta.ca) STAT 141 Final Review Winter 2015 11 / 20
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 2015 12 / 20
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 2015 13 / 20
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 2015 14 / 20
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 2015 15 / 20
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 2015 16 / 20
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 2015 17 / 20
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 2015 18 / 20
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. PF1 42. 4 Other topics: conditions (equal variance PF1 Q43; making conclusions (PF2 Q17); Bin Zou (bzou@ualberta.ca) STAT 141 Final Review Winter 2015 19 / 20
Chi-square Test (4 Q) 1 1+ Q on hypotheses, likely for a goodness-of-fit test. PF1 Q37 2 1 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 2015 20 / 20