Answers - Statistics Unlocking the Power of Data PDF

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Partial answers from the textbook - Statistics: Unlocking the Power of Data ...

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PARTIAL ANSWERS

UNIT A: Data CHAPTER 1 Section 1.1 Partial Answers 1.1 (a) (b) 1.3 (a) (b) 1.5 (a) (b) 1.7 1.9 1.11

1.13

1.15 1.17 1.19

1.21 1.23

1.25

The people who are asked Support the law or not; Categorical The teenagers in the sample At least five servings or not; Categorical The 10 beams Force at which each beam broke; Quantitative Explanatory: Years smoking; Response: Lung capacity Explanatory: Number of drinks; Response: Blood alcohol content (a) Year and HigherSAT are categorical; Other six are quantitative although Siblings might be either (b) Answers will vary (c) Answers will vary (a) Five variables are categorical; All others are quantitative (b) Answers will vary Lakes; Estrogen and fertility level; Both quantitative Explanatory: father’s diet (categorical); Response: daughter metabolic status (categorical) First study: Students; Smoked hookah or not; Categorical Second study: People in a hookah bar; Three variables; All quantitative Third study: Smoke samples; Three variables; All quantitative Short answer not appropriate (a) One categorical variable, value = flavor name (b) Four categorical variables, value = yes/no (c) Four variables with rank for each flavor, could be treated as quantitative or categorical (d) Four quantitative variables with rating for each flavor Cases: people; Variables: measure of wealth, measure of happiness

Section 1.2 Partial Answers 1.27 Sample 1.29 Population 1.31 Sample: The 120 people; Population: Many possible answers 1.33 Sample: 500 Canadian adults; Population: All Canadian adults 700

1.35 Sample: cookies in one Chips Ahoy package; Population: All Chips Ahoy cookies 1.37 (a) 100 college students asked (b) All Americans (c) College students 1.39 (a) The 1500 people contacted (b) All US residents (c) Residents of Minnesota 1.41 Yes 1.43 No 1.45 No 1.47 Biased; sampling bias 1.49 Biased; sampling bias 1.51 Biased; volunteer sample 1.53 (a) Cases: 6000 restroom patrons observed; 3 categorical variables: Wash, Gender, Location (b) People not always honest in self-reporting 1.55 No, volunteer sample is biased; Sample: 38,485 people who voted 1.57 Yes, it is a random sample 1.59 (a) US residents (b) US businesses and government agencies (c) i. CES ii. CPS iii. CPS 1.61 Answers will vary 1.63 (a) Short answer not appropriate (b) Answers will vary Section 1.3 Partial Answers Neither Association Association and causation Population Snow Gender Experiment Observational study Experiment Snow is associated with colder days; Shoveling snow leads to back pain 1.85 Age or grade level 1.87 (a) Students; type of dorm (categorical); number of hook-ups (quantitative) (b) Explanatory: type of dorm; Response: number of hook-ups (c) Yes (d) Yes (e) Observational studies (f) Students self-select the type of dorm (g) No!

1.65 1.67 1.69 1.71 1.73 1.75 1.77 1.79 1.81 1.83

PARTIAL (h) Assuming causation when he shouldn’t be 1.89 (a) Experiment (b) Explanatory: color (categorical); Response: rating (quantitative) (c) Short answer not appropriate (d) Yes 1.91 (a) Explanatory: amount of rest; Response: attractiveness rating (b) Matched pairs experiment (c) Yes, this is an experiment 1.93 (a) Explanatory: amount of sleep; Response: growth in height (b) Short answer not appropriate (c) Not ethical to deprive children of sleep 1.95 Short answer not appropriate CHAPTER 2 Section 2.1 Partial Answers 2.1 2.3 2.5 2.7 2.9

2.11 2.13

2.15

2.17

2.19

2.21 2.23

2.25

0.4669, or 46.69% 0.1972, or 19.72% p = 0.124 pˆ = 0.62 Academy Award: 0.086; Nobel Prize: 0.412; Olympic gold medal: 0.503 Short answer not appropriate (a) Sample: 119 players; Population: All RPS players; Variable: the option played (b) 0.555 (Rock), 0.328 (Paper), 0.118 (Scissors) (c) Paper (d) Scissors (a) Variable: tylosin or not; Individuals: 20 dust samples (b) Short answer not appropriate (c) Short answer not appropriate (d) Short answer not appropriate (a) Dog correct or not and type of sample (b) Short answer not appropriate (c) 0.917; 0.974 (d) 0.529 (a) Males, 14% to 9.5% (b) 11.9% (c) 37.2% Cardiac arrest: 9.5%; Other: 1.1% (a) Experiment (b) Single-blind (c) Two variables, both categorical (d) Short answer not appropriate (e) 75% (f) pˆ E − pˆ S = 0.60 − 0.20 = 0.40 (g) Yes (a) Observational study; No (b) Women attempting to become pregnant

ANSWERS

(c) pˆ = 0.36, pˆ s = 0.28, pˆ ns = 0.38 (d) pˆ ns − pˆ s = 0.10 2.27 (a) 68.6% (b) 58.0% (c) 15.7% (d) 7.2% 2.29 (a) Females; Graph (a) (b) Approximately equal; Graph (a) (c) Males; Graph (b) (d) Females; Graph (b) 2.31 Graph (b) Section 2.2 Partial Answers 2.33 F 2.35 B, C, E 2.37 E, G: Mean ≈ Median; F: Mean > Median; H: Mean < Median 2.39 Answers will vary 2.41 Answers will vary 2.43 (a) x = 11.2 (b) m = 12 (c) No outliers 2.45 (a) x = 24.5 (b) m = 20 (c) 58 is a likely outlier 2.47 x = 2386 2.49 µ = 41.5 2.51 (a) Mean (b) Mean = 7.2 mg/kg; Median = 3.65 mg/kg 2.53 (a) Population (b) Skewed to the right, with one outlier (c) About 4 million (d) About 6 million 2.55 (a) Skewed to the left (b) 6.5 (c) Smaller 2.57 (a) x¯ = 26.6; m = 16 (b) x¯ = 16.78; m = 15 (c) Affects the mean more than the median 2.59 (a) Skewed to the right (b) Mean = 39.1; Median = 10 2.61 mH − mC = −399 2.63 Answers will vary 2.65 m = 1; x = 3.2 Section 2.3 Partial Answers 2.67 (a) x = 17.36; s = 5.73 (b) (10, 13, 17, 21, 28) 2.69 (a) x = 10.4; s = 5.32 (b) (4, 5, 11, 14, 22) 2.71 (a) x = 9.05; s = 5.74 (b) (0, 5, 8, 12, 40) 2.73 (a) s = 5: Histogram A (b) s = 1: Histogram B (c) s = 3: Histogram C 2.75 (a) II (b) V (c) IV (d) I (e) III 2.77 x ≈ 500; s between 20 and 25 2.79 Approximately (440, 485, 500, 515, 560) 2.81 62; 73 2.83 Symmetric

(f) VI

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702 2.85 2.87 2.89 2.91 2.93 2.95

2.97

2.99 2.101 2.103

2.105 2.107

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2.111 2.113 2.115 2.117 2.119

PARTIAL

ANSWERS

Skewed left 1.72, standard deviations above mean −2.96, standard deviations below the mean 150 to 250 980 to 1020 (a) x ≈ 53 (b) s ≈ 5 (c) x = 52.875; s = 5.07 (a) (17.8, 22.175, 24.4, 26.825, 30.9) (b) Range = 13.1; IQR = 4.65 (c) Between 17.8 and 22.175; Between 24.4 and 26.825 (a) 4, 0, 3, −2, −17 (b) Mean −2.4; StDev 8.5 (a) 0.39◦ C to 4.23◦ C (b) 2.7 standard deviations above mean (a) x = 0.272; s = 0.237 (b) 2.44 (c) (0.073, 0.118, 0.158, 0.358, 0.851) (d) Range = 0.778; IQR = 0.24 No, not bell-shaped FGPct: 0.868 Points: 2.698 Assists: 1.965 Steals: 1.771 Most impressive: Points Least impressive: FGPct (a) x = 65.89; s = 18.29 (b) x = 26.18; s = 3.41 (c) Short answer not appropriate (a) x = 13.15 years; s = 7.24 years (b) 3.71 standard deviations above the mean (a) 5, 5, 5, 5, 5, 5 (b) 1, 1, 1, 9, 9, 9 Short answer not appropriate Short answer not appropriate (a) Estimate = 19, actual = 12.2 (b) Estimate = 8, actual = 5.741 (c) Estimate = 7.8, actual = 7.24

2.135 2.137

2.139 2.141 2.143

2.145 2.147

Section 2.5 Partial Answers 2.149 2.151 2.153 2.155 2.157 2.159 2.161 2.163 2.165 2.167 2.169 2.171 2.173

Section 2.4 Partial Answers 2.121 (a) W (b) X (c) Y (d) Z 2.123 (a) Skewed right (b) No outliers (c) About 50; Answers may vary 2.125 (a) Approximately symmetric (b) 3 low outliers and 2 high outliers (c) About 1200 2.127 (a) Outliers: 15, 20 (b) Short answer not appropriate 2.129 (a) Outliers: 28, 30 (b) Short answer not appropriate 2.131 No outliers; Less than 7 2.133 (a) Drama; Horror

(b) Drama; Action (c) Thriller, 24; Action & Comedy, 93 (d) Action (a) Four outliers, at 402, 447, 511, 536 (b) Short answer not appropriate (a) Seven outliers: all greater than 3264 (b) No low outliers (c) Short answer not appropriate Vitamin use has little effect on retinol levels Blood pressures slightly higher for survivors; Descriptions will vary (a) Short answer not appropriate (b) Low: mean 68.50 bpm, stdev 16.23; Medium: mean 58.67 bpm, stdev 14.28; High: mean 58.17 bpm, stdev 13.78 (c) Experiment Answers will vary Answers will vary

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(b) (d) (c) (d) Positive Negative Negative Short answer not appropriate r = 0.915 (a) 3; 27.3% (b) Eisenhower; Nixon Exp: roasting time, Resp: amount of caffeine; Negative association Positive (a) Negative (b) Bottom right; top left (c) Vermont; Mississippi, Kentucky, or Oklahoma (d) Population; ρ (e) ρ = −0.605 (f) No (g) No (h) Colorado (a) Three quantitative variables (b) Negative; Yes (c) Positive; No; Yes (a) Positive: spend time on both or neither; Negative: spend time on one or the other but not both (b) Lots of exercise and little TV; Lots of time on both; Very little time doing either; Lots of TV and little exercise (c) Lots of TV and little exercise; Lots of exercise and little TV

PARTIAL (d) Almost no linear relationship 2.179 (a) Short answer not appropriate (b) −0.096 (c) 0.562 (d) Yes 2.181 Type of drink is categorical 2.183 Short answer not appropriate 2.185 (a) Short answer not appropriate (b) No evidence of an association (c) Pirates of the Caribbean, 61; Harry Potter and the Deathly Hallows, Part 2 (d) 0.084 Section 2.6 Partial Answers 2.187 (a) 57.18 inches; 2.82 inches (b) Grow about 2.74 inches per year (c) Expected length of newborn is 24.3 2.189 (a) 153.5 lbs; −3.5 lbs (b) Weight goes up 11.7 for one more hr/wk (c) If never train, can lift 95 lbs ˆ = 0.395 + 0.349X 2.191 Y ˆ = 111.7 − 0.84X 2.193 Y 2.195 (a) Year; CO2 (b) Very strong linear relationship (c) r = 0.993; Yes &2 = −2571 + 1.47(Year) (d) CO (e) CO2 going up 1.47 ppm per year (f) −2571; No; Can’t be negative (g) 373.41 ppm; 398.4 ppm (h) 6.08 2.197 (a) Mild positive linear relationship (b) Larger in 2007; Negative in 2010 (c) r = 0.692 ! (d) HotDogs = −3385 + 1.72 · Year (e) 1.72 more hot dogs eaten each year (f) 75.64 hot dogs (g) Extrapolating too far away 2.199 Short answer not appropriate 2.201 190 lbs, 40% body fat; Predicted body fat = 20%; Residual 20 2.203 (a) 13.35%; 22.1% (b) Short answer not appropriate (c) −8.525% 2.205 (a) Land area; Percent rural (b) 0.60 ! (c) Rural = 28.99 + 0.079(LandArea) (d) No (e) Uzbekistan (UZB) (f) 752%; Not reasonable; Extrapolate too far 2.207 (a) Short answer not appropriate (b) Harry Potter and the Deathly Hallows, Part 2 (c) r = 0.904 ! (d) WorldGross = −8.7 + 7.70 · OpeningWeekend

ANSWERS

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(e) 376.3 million dollars 2.209 Answers will vary UNIT A: Essential Synthesis Partial Answers A.1 (a) Experiment (b) Subjects can see which treatment (c) Sample is 46 subjects; Population answers may vary (d) One quantitative, one categorical (e) Side-by-side boxplots A.3 (a) The students/computers; 45; Not random (b) Observational study (c) Four variables, all quantitative (d) Histogram, dotplot, or boxplot; Boxplot (e) Scatterplot; Correlation; Negative (f) No, not an experiment (g) Explanatory: time on distracting websites; Response: exam score (h) Randomized experiment A.5 Answers will vary A.7 (a) Sample: 86 patients; Population: all people with bladder cancer (b) Two categorical variables (c) Experiment (d) Two-way table (e) Yes, the drug appears to be more effective A.9 Answers will vary UNIT A: Review Exercise Partial Answers A.11 (a) Sample: 200 patients; Population: All ICU patients (b) Age, Systolic, HeartRate (c) Answers will vary (d) Answers will vary A.13 (a) Observational study (b) Explanatory: fish consumption; Response: test score (c) Answers will vary (d) No A.15 Short answer not appropriate A.17 (a) Students; 70 (b) Treatment group; Three ratings (c) Experiment (d) Short answer not appropriate (e) Side-by-side boxplots; Scatterplot A.19 Answers will vary A.21 (a) Experiment (b) Short answer not appropriate (c) xS − xN = 1.9 (d) Yes A.23 (a) Sample: 48 participants; Population: All people; Variable: Whether a person’s lie is detected (b) pˆ = 0.35 (c) No

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ANSWERS

A.25 Yes; x ≈ 7; s ≈ 2 A.27 (a) There are likely low outliers (b) Short answer not appropriate (c) Skewed to the left A.29 (a) Sample: The 1917 people; Population: All cell phone users (b) Relative frequency (c) Skewed to the right (d) m = 5; x = 13.10 A.31 (a) Skewed to the right (b) x = 13.7 min; m = 2.5 min A.33 53.3% A.35 Answers will vary A.37 Teens: No outliers; 80s: Two outliers at 190 A.39 (a) x ≈ 100; s ≈ 25 (b) About 60 (c) About 150 A.41 (a) Short answer not appropriate (b) r = −0.071 (c) No A.43 (a) Short answer not appropriate (b) r = −0.189 (c) Short answer not appropriate (d) r = 0.836 (e) Very substantial effect A.45 (a) Positive; Positive (b) Calories and fat (c) Fat ≈ 240 grams; Fiber ≈ 23 grams; Extreme for fat not fiber A.47 (a) Short answer not appropriate (b) 26.92; 33.46 (c) 11.77 A.49 (a) Negative linear trend (b) Two outliers at left: Bogut and Jordan (c) −0.402 ! (d) FGPct = 0.647 − 0.236 · FTPct (e) 0.482

(b) (c) 3.25 (a) (b)

3.27 3.29

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3.33 3.35 3.37

Section 3.2 Partial Answers 3.39 3.41 3.43 3.45 3.47 3.49 3.51

UNIT B: Understanding Inference CHAPTER 3 Section 3.1 Partial Answers 3.1 3.3 3.5 3.7 3.9 3.11 3.13 3.15 3.17 3.19 3.21 3.23

Parameter; µ Statistic; pˆ Statistic; x µ = 324.2 r = 0.037 ρ = −0.131 µ = 85; SE ≈ 20 p = 0.80; SE ≈ 0.03 (a) (i) (b) (i) (c) (ii) (a) (ii) (b) (ii) (c) (iii) p; p; ˆ 0.55 (a) µ = 30, parameter; x = 27.90, statistic

Bell-shaped and centered at 30 1000 dots; each represents a mean for n = 75 A: n = 20; B: n = 100; C: n = 500 Not surprising; Possible but unlikely; Extremely unlikely (c) Not surprising; Not surprising; Possible but unlikely (d) As sample size goes up, accuracy increases pa − pt ; pˆ a − pˆ t ; best estimate = −0.15 (a) 0.05 (b) About 0 to 0.12; About 0.25 to 0.7 (c) SE ≈ 0.02; SE ≈ 0.005 (d) Yes; No (a) Answers will vary (b) Answers will vary (c) µ = 26.46 points (d) Roughly symmetric and centered at 26.46 Minimum ≈ 8 to maximum ≈ 50; std.dev. about 7: answers will vary (a) p = 0.150 (b) Bell-shaped; centered at 0.150 (a) SE ≈ 0.11; largest pˆ ≈ 0.6, off by 0.45 (b) SE ≈ 0.08; largest pˆ ≈ 0.4, off by 0.25 (c) SE ≈ 0.05; largest pˆ ≈ 0.3, off by 0.15 (d) Increasing n increases accuracy

3.53 3.55 3.57

3.59 3.61 3.63

22 to 28 0.57 to 0.67 (a) Yes (b) Yes (c) No 0.24 to 0.40; p 0.30 to 0.38; ρ 1.8 to 4.2; µ1 − µ2 (a) Statistic; pˆ = 0.30 (b) Proportion, p, of all US young people arrested by 23; pˆ = 0.30 (c) 0.29 to 0.31 (d) Very unlikely Short answer not appropriate Point estimate: pˆ = 0.28; Margin of error: ±0.018; 95% CI: 0.262 to 0.298 (a) Short answer not appropriate (b) Not the same; Game players are faster (c) Short answer not appropriate (d) Yes; Similar accuracy is plausible (a) No (b) Yes (c) Yes (d) No 46.2 to 55.8 seconds; No, Yes Parameter: p1 − p2 ; Point estimate: pˆ 1 − pˆ 2 = 0.44;

PARTIAL 95% CI: 0.16 to 0.72; Not likely Section 3.3 Partial Answers 3.65 (a) No (b) No (c) Yes (d) No (e) Yes 3.67 Point estimate ≈ 0.7; SE ≈ 0.1; Interval: 0.5 to 0.9; Parameter: p 3.69 Point estimate ≈ 0.4; SE ≈ 0.05; Interval: 0.3 to 0.5; Parameter: ρ 3.71 SE ≈ 0.048; Interval: 0.254 to 0.446 3.73 SE ≈ 0.022; Interval: 0.236 to 0.324 3.75 (a) pˆ = 0.149 (b) SE ≈ 0.028 (c) 0.093 to 0.205 (d) Yes 3.77 (a) x = 67.59; s = 50.02 (b) Short answer not appropriate (c) Bell-shaped, centered at 67.59 (d) $45.79 to $89.39 3.79 (a) pˆ = 0.767 (b) Short answer not appropriate (c) Bell-shaped and centered at 0.767; SE ≈ 0.077 (d) 0.613 to 0.921 3.81 (a) SE = 0.015 (b) 0.12 to 0.18 3.83 (a) µD , mean population time savings (b) Short answer not appropriate (c) Sample mean for n = 24 values (d) Slight rightskew, centered at 61 (e) Standard deviation of the bootstrap statistics (f) 54.8 to 67.2 seconds 3.85 (a) r = 0.807 (b) Bell-shaped, centered near 0.81 (c) Margin of error = 0.071, (0.736,0.878) (d) Short answer not appropriate 3.87 27.1 to 71.1 minutes Section 3.4 Partial Answers 3.89 3.91 3.93 3.95 3.97 3.99 3.101 3.103 3.105 3.107 3.109

(a) 25 (b) 50 (c) 10 (d) 5 C A B Approximately 0.66 to 0.78; Answers may vary Approximately 0.34 to 0.42; Answers may vary 29.4 to 76.7 Approximately 0.467 to 0.493; Yes 3.47 to 4.23; Results are similar (a) pˆ m − pˆ f = 0.045; Males (b) −0.04 to 0.13 (a) xt − xc = 17.12 (b) µt − µc (c) 4.17 to 29.70

ANSWERS

(d) −3.30 to 37.04 (e) Yes; No 3.111 30,100 to 228,300 sq km 3.113 (a) Short answer not appropriate (b) µatl − µstl ; xatl − xstl = 7.14 minutes (c) Short answer not appropriate (d) 4.89 to 9.39 minutes 3.115 (a) Symmetric and bell-shaped; CI for σ : about 7 to 14 thousand dollars (b) Not symmetric and bell-shaped; Not appropriate to use to find a CI CHAPTER 4 Section 4.1 Partial Answers 4.1 (a) Sample A (b) Sample C 4.3 (a) Sample A (b) Samples B and C 4.5 H0 : µA = µB vs Ha : µA = µB 4.7 H0 : µ = 50 vs Ha : µ < 50 4.9 H0 : pm = pf vs Ha : pm > pf 4.11 H0 : p = 0.20 vs Ha : p < 0.20 4.13 H0 : µf = µu vs Ha : µf = µu 4.15 (a) valid (b) invalid (c) invalid (d) invalid 4.17 (a) H0 : µb = µw vs Ha : µb > µw (b) 17.36 and 18.72; Yes, Yes (c) 23.60 and 19.17; Yes, Probably not (d) Drinking beer attracts mosquitoes! (e) Yes, since it was an experiment 4.19 (a) H0 : µe = µs vs Ha : µe < µs (b) H0 : µe = µs vs Ha : µe > µs (c) H0 : ρ = 0 vs Ha : ρ < 0 4.21 H0 : µm = µf vs Ha : µm > µf 4.23 H0 : ρ = 0 vs Ha : ρ > 0 4.25 H0 : µ = 50 vs Ha : µ > 50 4.27 (a) H0 : ρ = 0 vs Ha : ρ = 0 (b) r = 0.75 (c) Same (just opposite directions) 4.29 (a) H0 : µ = 3800 vs Ha : µ > 3800 (b) H0 : µ = 3800 vs Ha : µ < 3800 4.31 Test; H0 : p = 0.10 vs Ha : p > 0.10 4.33 Test; H0 : µD = 0 vs Ha : µD < 0 OR: H0 : µR = µL vs Ha : µR < µ L 4.35 Test, H0 : p = 0.5 vs Ha : p > 0.5 4.37 (a) H0 : pc = pf vs Ha : pc = pf (b) pˆ c = 0.608; pˆ f = 0.580; Yes (c) pˆ c = 0.752; pˆ f = 0.480 (d) Sample B 4.39 (a) H0 : ρ = 0 vs Ha : ρ > 0 (b) Yes (c) No (d) Placebo could give as extreme a correlation Section 4.2 Partial Answers 4.41 0.08 4.43 0.007 4.45 (a) 0.01 (b) 0.30 (c) 0.05

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ANSWERS

4.47 (a) 0.01 (b) 0.30 4.49 (a) Short answer not appropriate (b) D = −1.3 4.51 (a) Short answer not appropriate (b) Both give same evidence 4.53 UV: 0.002; Vitamin D: 0.472 4.55 (a) 0.11 (b) 0.03 (c) (b) D = 2.4, p-value = 0.03 4.57 (a) Short answer not appropriate (b) D = 0.2, p-value = 0.392 D = −0.4, p-value = 0.066 (c) 0.008 4.59 (a) Relatively small p-value (b) Relatively large p-value (c) Relatively small p-values 4.61 Short answer not appropriate 4.63 (a) Once (b) Yes, p-value is very small (c) No 4.65 (a) H0 : p = 1/6 vs Ha : p > 1/6 (b) p = 1/6, the proportion for H0 (c) pˆ = 0.1; Answers will vary (d) Left (e) Right (f) p-value > 0.50

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Section 4.4 Partial Answers 4.107 4.109 4.111 4.113 4.115 4.117 4.119 4.121 4.123

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Section 4.3 Partial Answers 4.67 4.69 4.71 4.73 4.75

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Reject H0 Do not reject H0 Yes; Yes; No Yes; Yes; Yes (a) I. 0.0875 (b) IV. 0.00003 (c) III. 0.0217 (d) II. 0.5457 Test A No 1% (a) Evidence that price affects effectiveness (b) Short answer not appropriate (a) H0 : p = 0.5 vs Ha : p = 0.5 (b) Do not reject H0 ; No (c) Reject H0 ; Yes (a) p-value < 0.05 (b) No (c) Yes (d) No, not an experiment (a) Yes (b) Very strong (c) Yes, this is an experiment (a) Not valid (b) Valid (c) Valid Small, α = 0.01 Large, α = 0.10

Large, α = 0.10 Short answer not appropriate Short answer not appropriate Short answer not appropriate (a) Reject H0 ; No error or Type I error (b) Do not reject H0 ; No error or Type II error (c) Need to know the actual value of the parameter

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pˆ r pˆ 1 − pˆ 2 10; Right-tail 0; Two-tail p-value ≈ 0.10 p-value ≈ 0.01 p-value ≈ 0.12 (a) H0 : p = 0.5 vs Ha : p > 0.5 (b) Answers will ...