Statistical Inference

Problem 1

True or false: For a population proportion confidence interval, we use $\mathrm{z}$ -distribution, not $\mathrm{t}$ -distribution.

See Solution

Problem 2

Identify which statements about confidence intervals and distributions are true or false: 1) z vs t for population proportion, 2) degrees of freedom, 3) known $\sigma$ and Z, 4) unknown $\sigma$ and S, 5) t vs z for population proportion.

See Solution

Problem 3

Find the test statistic $z$ for a sample mean of 84, size 49, standard deviation 14, testing if mean > 80 at $\alpha = 0.05$ .

See Solution

Problem 4

Identify which statements are true or false regarding confidence intervals and distributions.

See Solution

Problem 5

Test if the mean score of sober subjects is 35 using scores: mean = 41, std dev = 3.7, n = 20, significance = 0.01.
Test if the proportion of women (65%) favoring gun control is higher than men (60%) using samples of 360 women and 220 men, significance = 0.05.

See Solution

Problem 6

Commuters and parking spaces data: a) Find the correlation coefficient. b) Find critical values for $r$ . c) Check for significant correlation at 0.05 level. d) State the conclusion.
CPI and subway fare data: a) Find regression equation with CPI as $x$ . b) Predict subway fare for CPI = 182.5.

See Solution

Problem 7

Construct a 95% confidence interval for the standard deviation of 23 PG-rated movies with mean 120.8 and SD 22.9. Show steps.

See Solution

Problem 8

A researcher tests if a diet lowers blood pressure ( $\mathrm{mm} \mathrm{Hg}$ ) for those with high blood pressure. Use $\alpha = 0.01$ to compare means from treatment (n=35, $\bar{x}=189.1$ , s=38.7) and control (n=28, $\bar{x}=203.7$ , s=39.2).
a) State null and alternative hypotheses. b) Calculate test statistic and $\mathrm{p}$ -value. c) Make a decision. d) Interpret conclusion. e) Find and interpret the 99% confidence interval.

See Solution

Problem 9

1. Given commuter and parking space data, find the correlation coefficient, critical values for $r$ , and check significance at 0.05.
2. For CPI and subway fare data, find the regression equation with CPI as $x$ and predict fare for CPI = 182.5.

See Solution

Problem 10

Test if the mean score of sober subjects is 35 using a sample mean of 41, SD of 3.7, at 0.01 significance level.
Also, test if the proportion of women (65%) favoring stricter gun control is higher than men (60%) at 0.05 significance level.

See Solution

Problem 11

Construct a confidence interval for LDL cholesterol changes: mean = 3.2, SD = 18.6. What is the best point estimate?

See Solution

Problem 12

A chemist studies how carbon atoms in hydrocarbons affect energy release during combustion. Estimate $\theta_{0}$ and $\theta_{1}$ for $y = \theta_{0} + \theta_{1} x$ . Options: $\theta_{0}=-569.6, \theta_{1}=530.9$ ; $\theta_{0}=-1780.0, \theta_{1}=530.9$ ; $\theta_{0}=-569.6, \theta_{1}=-530.9$ ; $\theta_{0}=-1780.0, \theta_{1}=-530.9$ .

See Solution

Problem 13

Find Sharpe's measure for Ella's stock with beta 1.34, std. dev. 16.4%, return 14.8%, market risk premium 8.5%, market return 12.0%.

See Solution

Problem 14

How many people were unemployed in Africa in 2014 if the number is expected to reach 61 million in 2024, a $24.5 \%$ increase? Round to the nearest million.

See Solution

Problem 15

Construct a confidence interval for garlic's effect on LDL cholesterol. Mean change: 3.2, SD: 18.6. Find point estimate and $95\%$ CI.

See Solution

Problem 16

1. Given commuter and parking space data, find the correlation coefficient, critical values for $r$ , and test for significance at 0.05.
2. For CPI and subway fare, find the regression equation with CPI as $x$ and predict fare for CPI = 182.5.

See Solution

Problem 17

Explain $k$ -fold cross-validation implementation and its pros/cons vs. validation set approach and LOOCV.

See Solution

Problem 18

Test if the mean height of 5-year-olds is > $95 \mathrm{~cm}$ using a sample mean of $100 \mathrm{~cm}$ , $n=20$ , $\sigma=6 \mathrm{~cm}$ , at $\alpha=0.01$ . a) State hypotheses, b) find test statistic, c) find P-value, d) make decision, e) conclude.

See Solution

Problem 19

7.- A pro shop has a probability distribution for golf ball orders. a) Find the probability of ordering at most 2 golf balls. b) Find the probability of ordering at least one golf ball. c) Find the mean.
8.- A teacher claims the mean height of 5-year-olds is more than 95 cm. a) State the null and alternative hypothesis. b) Find the test statistic. c) Find the P-value or critical points. d) Make a decision using P-value or critical values. e) State your conclusion.

See Solution

Problem 20

Test if the proportion of men who smoke ( $p_m$ ) is greater than that of women ( $p_w$ ) using a 0.05 level. Find hypotheses, test statistic, P-value, decision, and conclusion. Also, find the $90\%$ confidence interval. Bonus: Predict $y$ for $x=32$ using $\hat{y}=5.50+1.91x$ .

See Solution

Problem 21

A songwriter studies the correlation between song length (in seconds) and weeks at number one. Use significance level 0.05 to analyze:
a) Set null and alternative hypotheses. b) Calculate $r$ , statistic value $t$ , and $p$ -value. c) Find critical values for $r$ . d) Decide using p-value or critical values.

See Solution

Problem 22

Find the $z$ -score for a person who scored 616 on an exam with mean 500 and standard deviation 40.

See Solution

Problem 23

Calculate the correlation coefficient between annual growth of National Income and Gross Domestic Saving from 1992-2002.

See Solution

Problem 24

Conjecture the percentage of the population with type O blood from a sample result of 0.42. Is it descriptive or inferential statistics?

See Solution

Problem 25

Students were surveyed on video game time and test averages. Is the correlation negative or weak? True/False statements provided.

See Solution

Problem 26

Analyze the frequency table of art styles to determine if there's an association between art type and style.

See Solution

Problem 27

A city inspector found that $41.1\%$ of 500 buildings met readiness conditions with a margin of error of $\pm 5\%$ . What must be true?

See Solution

Problem 28

Find the confidence interval for the true mean SAT score given a mean of 482 and a margin of error of 15.

See Solution

Problem 29

Which of these is a statistical question? A. Lunch period length? B. Oldest student age? C. Classrooms count? D. Ages of classmates?

See Solution

Problem 30

Elise has two loans: a \$20,000 fixed-rate at 4.5\% and a \$20,000 variable-rate at 4.15\%. Which is more predictable in total cost?

See Solution

Problem 31

Is the frequency distribution normal based on the criteria? Choose A, B, or C based on the given temperature ranges and frequencies.

See Solution

Problem 32

Calculate the correlation coefficient $r$ and the regression line for the given sea level pressure and wind speed data. Then predict wind speed for 977 millibars. Round appropriately.

See Solution

Problem 33

Determine the correlation coefficient $r$ , regression line, and predict weight for a 124-inch alligator. Is it valid for 20 inches?

See Solution

Problem 34

Find the line of best fit for the data: $(x, y) = (1, 9.6), (2, 6.3), (3, 2.8), (4, 8.73), (5, 5.9), (6, 1.2)$ . Interpret the correlation coefficient.

See Solution

Problem 35

Identify a Type II error from these options: rejecting $H_0$ when $H_0$ is false, true, or not rejecting when true/false.

See Solution

Problem 36

What term describes findings in an experiment that reach conventional statistical significance? Options: nonsignificant, insignificant, significant, unworthy.

See Solution

Problem 37

Is there a link between liking a TV show and viewer age? (a) Find expected adults who dislike: $20.13$ . (b) Calculate $\chi^{2}$ test statistic: $\chi^{2}=\sum \frac{(observed - expected)^{2}}{expected}$ .

See Solution

Problem 38

Predict heart weight (g) from body weight (kg) using regression.
(i) (a) Model: $\hat{y}=-0.339+4.028 x$ (b) Intercept: Expected heart weight at 0 kg is $-0.339$ g. (c) Slope: Each kg increases heart weight by 4.028 g. (d) $R^{2}$ : Body weight explains $64.65\%$ of heart weight variability. (e) Correlation coefficient: $0.8049$

See Solution

Problem 39

Calculate expected values under the null hypothesis for party affiliation and support of full-body scans.
(a) Expectation for Republicans not supporting: $48$ (b) Expectation for Democrats supporting: $?$ (c) Expectation for Independents unsure: $22$

See Solution

Problem 40

Analyze responses from 825 voters on oil drilling in CA. Perform a chi-square test for college grads vs non-grads at $\alpha = 0.05$ . State hypotheses, calculate test statistic (2 decimal places), and find $p$ -value (3 decimal places). Note data discrepancies.

See Solution

Problem 41

Survey skiers' preferences for ski areas. Test if preference is independent of skill level at $\alpha=0.05$ . Find test statistic and $p$ -value.

See Solution

Problem 42

A survey of 825 California voters examines opinions on offshore drilling. Perform a chi-square test with $H_{0}$ : no difference, $H_{A}$ : difference. Test statistic is 12.32; confirm and find the $p$ -value.

See Solution

Problem 43

Test if skier level and preferred ski area are independent at $\alpha = 0.05$ . Calculate test statistic, p-value, and conclusions.

See Solution

Problem 44

Find the slope of the best fit line for clubhead speeds (mph) and distances (yards) from 20 games data.

See Solution

Problem 45

Analyze the scatter plot of calories vs. fat in chicken sandwiches. What association is indicated by increasing grams and calories?

See Solution

Problem 46

Which aspect of a statistical study does the statement about cohabitation and divorce refer to: Inference, Design, or Description?

See Solution

Problem 47

A study of 27,000 individuals tested if a herbal supplement reduces asthma attacks. What aspects relate to design and description?

See Solution

Problem 48

What type of statistics is it when $90 \%$ of taste testers prefer the new coffee brand? Options: Investigation, Description, Design, Inference, None.

See Solution

Problem 49

A golfer has data on clubhead speeds (mph) and distances (yards) for 20 games. What analysis should be done: correlation, averages, or something else?

See Solution

Problem 50

A historian finds marriage records from 1800-1820. Answer these: a) Descriptive summary? b) Inference? c) Population? d) Is 26.1 a statistic or parameter?

See Solution

Problem 51

Are the populations the same if two different samples of 10 students support single sex classrooms? A. No, B. Yes, C. Yes, D. No.

See Solution

Problem 52

Two students sample 10 each to find support for single sex classrooms. Answer parts a and b about their populations.

See Solution

Problem 53

A historian finds marriage records (1800-1820) showing an average age of 26.1 years. Answer the following: a. What is the descriptive summary? b. What is the inference about the population? c. What population does this refer to? d. Is 26.1 a statistic or a parameter?

See Solution

Problem 54

Is the $31\%$ response from the poll a statistic or a parameter regarding voter opinions on immigration?

See Solution

Problem 55

A historian finds marriage records from $1800-1820$ showing an average age of 26.7. Answer these questions about the data.

See Solution

Problem 56

A historian estimates the average age at marriage of men (1800-1820): average age is 26.7 years, range is 25.8-27.6 years.
a. What summarizes the data? b. What infers about the population? c. What population is referred to? d. Is 26.7 a statistic or parameter?

See Solution

Problem 57

Is $55\%$ of seniors owning a vehicle a statistic or a parameter? Choose the correct explanation.

See Solution

Problem 58

Calculate the correlation coefficient $r$ , find the regression line, and predict the 5K time for $\mathrm{VO}_{2} \mathrm{max} = 24.79$ .

See Solution

Problem 59

Determine if the following values are parameters or statistics: a. 66% of MAT 120 students passed. b. Mean height of 228 males is 69.5 inches. c. 16% of a Stats class are freshmen. d. Mean daily Snapchat usage is 68 minutes.

See Solution

Problem 60

Calculate Spearman's rank correlation coefficient for the ranks: Geography: 6, 5, 4, 3, 2, 7, 1 and Economics: 7, 6, 2, 4, 1, 5, 3.

See Solution

Problem 61

Determine if there was discrimination against females based on the admission data: males admitted = 17, females admitted = 33. Total applicants: males = 25, females = 45.

See Solution

Problem 62

Who is more likely to be part-time: undergraduates (5,358) or graduates (1,769)? Choose the best answer.

See Solution

Problem 63

Analyze if hourly workers ( $31$ laid off) were more likely to be laid off than salaried ( $24$ laid off) using the data.

See Solution

Problem 64

Identify which preference table causes the Borda count winner to violate the majority criterion among candidates A, B, C.

See Solution

Problem 65

Compare IQs using z-scores: Test A (mean 100, SD 14) score 127 vs Test B (mean 100, SD 16) score 130. Who is higher?

See Solution

Problem 66

Estimate the number of employees out of 600 who read at least one book each month if $x$ out of 50 do.

See Solution

Problem 67

A survey shows that of students living >1 mile, $76\%$ ride a bike. Which conclusion is best?

See Solution

Problem 68

Find the correlation coefficient for the study hours (0, 0, 1, 2, 3, 5, 5, 8) and exam scores (61, 92, 67, 64, 75, 73, 82, 90). Options: -0.5, 0.5, -0.9, 0.9.

See Solution

Problem 69

Does a linear correlation between carbon dioxide concentration and global temperature imply causation? Choose A or B.

See Solution

Problem 70

Valerie's team of 30 rated her as "outstanding" at $83\%$ . Why might this result be biased? Choose 1 answer: A, B, C, or D.

See Solution

Problem 71

In Oak City, predict how many adults get news from newspapers based on a sample of 50,000. Round to the nearest whole number.

See Solution

Problem 72

Use the Grubbs test to check if $0.1189$ is an outlier in the data set $0.1123, 0.1087, 0.1139, 0.1112, 0.1189$ at $95\%$ confidence. Show your calculations.

See Solution

Problem 73

Given data on shopping habits by location, answer these:
A) Is living location "independent" or "dependent" of shopping choice?
B) Are observed values "same" or "different" from expected if dependent?
C) Expected urban shoppers at supermarket if independent? (Round to nearest tenth)
D) What is the $p$ -value for independence test? (Round to nearest tenth)
E) Is there evidence of a relationship between living location and shopping choice? "yes" or "no"

See Solution

Problem 74

Tina's survey of 600 students shows $53\%$ exercise over 30 mins daily. Why is this misleading? Choose one: outlier, small sample, biased sample, calculation error.

See Solution

Problem 75

If more driver's ed hours lead to fewer accidents, this indicates a $a(n)$ : A. negative correlation B. casual relationship C. ambiguous correlation D. positive correlation.

See Solution

Problem 76

Identify one fact about fibula lengths given the least relative frequency of 0.01 and highest frequency in 35-36 cm range.
A. About two-thirds of females have a length between 31 and 35 cm. B. About $25 \%$ of females have a length between 32 and 33 cm. C. About two-thirds of females have a length between 36 and 40 cm. D. About $25 \%$ of females have a length between 35 and 36 cm.

See Solution

Problem 77

If brand $A$ has scattered residuals and brand $B$ has clustered residuals, what can we conclude about their linearity?

See Solution

Problem 78

Which statement best reflects the relationship between correlation and causation? A, B, C, or D?

See Solution

Problem 79

Is the cost of fabric types proportional? Fabric A: \$31.25 for 5 sq. yd, Fabric B: \$71.50 for 11 sq. yd. Explain.

See Solution

Problem 80

Test if the average top speed of 87 cars (150 mph) differs from 145 mph using $H_0: \mu = 145$ at 1\% significance. Outcomes: 1-4.

See Solution

Problem 81

Calculate the correlation coefficient for $x = [28, 10, 21, 17, 24, -3, 16]$ and $y = [29, 21, -8, 22, -7, -10, -5]$ . Round to three decimal places.

See Solution

Problem 82

Find the cross-price elasticity of demand for strawberries when quantity drops from 1,800 to 1,550 as price falls from \$2.35 to \$2.15. Round to the nearest hundredth.

See Solution

Problem 83

If the correlation $r=0.63$ for variables $(x, y)$ , what can we say about the slope $b$ of the least-squares line?

See Solution

Problem 84

Given the weight regression $\text{Weight} = -115 + 3 \cdot 6(\text{Height})$ , which statements are true about height and weight?

See Solution

Problem 85

Find the slope, intercept, and correlation of $\mathrm{Y}$ from $\mathrm{X}$ using the data: $\mathrm{X} = [28, 64, 76, 97, 110]$ , $\mathrm{Y} = [200, 227, 178, 129, 113]$ .

See Solution

Problem 86

Is the student opinion survey on a tour program an observational or experimental study? If experimental, identify the controlled factor.

See Solution

Problem 87

What is the explanatory variable in Charles' survey on complaints and accidents? Choose from: number of complaints, accidents, people surveyed, none.

See Solution

Problem 88

Calculate the correlation $r$ between Amazon and B\&N prices for 14 textbooks. Round to the nearest 0.001.

See Solution

Problem 89

What evidence best supports the claim that more than $4\%$ of children carry a virus? Choose from the options given.

See Solution

Problem 90

If the correlation $r=0$ , what does this indicate about the relationship between two quantitative variables? A. Strong linear B. No linear C. Strong relationship D. No relationship

See Solution

Problem 91

Given the weight prediction formula $\text{Weight} = -115 + 3.6 \text{(Height)}$ , which statements are true? A. I only B. II and III only C. I and II only D. III only E. II only. Select one.

See Solution

Problem 92

A) What percent of treatment group patients were pain free after 24 hours? B) What percent of control group patients were pain free?

See Solution

Problem 93

1a. Are egg consumption and population size proportional in Republica and the U.S.? Show calculations and state your conclusion. 1b. If proportional, how many eggs would 86 million people consume? If not, explain which country prefers eggs more.

See Solution

Problem 94

Fit a regression line to the data and find the correlation coefficient. Predict life expectancy in 2020 using $x$ as decades after 1900. Choose the correct line: A. $y=48.08 x+0.750$ , B. $y=0.750 x-48.08$ , C. $y=0.750 x+48.08$ , D. $y=48.08$ .

See Solution

Problem 95

Fit a regression line to the data, find the correlation coefficient, and predict life expectancy in 2020 using $x$ as decades after 1900. Choose the correct regression line: A. $y=48.08 x+0.750$ B. $y=0.750 x-48.08$ C. $y=0.750 x+48.08$ D. $y=48.08$ . Round the correlation coefficient to three decimal places.

See Solution

Problem 96

Find the travel time $x$ such that $17.36\%$ of Abby's 60 days have a travel time of at least $x$ , given mean $35.6$ and SD $10.3$ . Round to two decimal places.

See Solution

Problem 97

Find the proportion of SAT scores above 1600, given a mean of 1021 and standard deviation of 214. Round to four decimal places.

See Solution

Problem 98

Calculate the correlation coefficient for the sets $x = \{28, 10, 21, 17, 24, -3, 16\}$ and $y = \{29, 21, -8, 22, -7, -10, -5\}$ .

See Solution

Problem 99

Find the residual for a 29 g chick from an egg with a breadth of 40 mm using the equation $\hat{y}=-47+2x$ .

See Solution

Problem 100

Estimate the total beetle population if Joe marked 590 beetles and found 59 marked in a catch of 2,000.

See Solution

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162

Statistical Inference

Problem 1

True or false: For a population proportion confidence interval, we use z\mathrm{z}z-distribution, not t\mathrm{t}t-distribution.

Problem 2

Identify which statements about confidence intervals and distributions are true or false: 1) z vs t for population proportion, 2) degrees of freedom, 3) known σ\sigmaσ and Z, 4) unknown σ\sigmaσ and S, 5) t vs z for population proportion.

Problem 3

Find the test statistic zzz for a sample mean of 84, size 49, standard deviation 14, testing if mean > 80 at α=0.05\alpha = 0.05α=0.05.

Problem 4

Identify which statements are true or false regarding confidence intervals and distributions.

Problem 5

Test if the mean score of sober subjects is 35 using scores: mean = 41, std dev = 3.7, n = 20, significance = 0.01. Test if the proportion of women (65%) favoring gun control is higher than men (60%) using samples of 360 women and 220 men, significance = 0.05.

Problem 6

Commuters and parking spaces data: a) Find the correlation coefficient. b) Find critical values for rrr. c) Check for significant correlation at 0.05 level. d) State the conclusion. CPI and subway fare data: a) Find regression equation with CPI as xxx. b) Predict subway fare for CPI = 182.5.

Problem 7

Construct a 95% confidence interval for the standard deviation of 23 PG-rated movies with mean 120.8 and SD 22.9. Show steps.

Problem 8

Problem 9

1. Given commuter and parking space data, find the correlation coefficient, critical values for rrr, and check significance at 0.05. 2. For CPI and subway fare data, find the regression equation with CPI as xxx and predict fare for CPI = 182.5.

Problem 10

Test if the mean score of sober subjects is 35 using a sample mean of 41, SD of 3.7, at 0.01 significance level. Also, test if the proportion of women (65%) favoring stricter gun control is higher than men (60%) at 0.05 significance level.

Problem 11

Construct a confidence interval for LDL cholesterol changes: mean = 3.2, SD = 18.6. What is the best point estimate?

Problem 12

Problem 13

Find Sharpe's measure for Ella's stock with beta 1.34, std. dev. 16.4%, return 14.8%, market risk premium 8.5%, market return 12.0%.

Problem 14

How many people were unemployed in Africa in 2014 if the number is expected to reach 61 million in 2024, a 24.5%24.5 \%24.5% increase? Round to the nearest million.

Problem 15

Construct a confidence interval for garlic's effect on LDL cholesterol. Mean change: 3.2, SD: 18.6. Find point estimate and 95%95\%95% CI.

Problem 16

1. Given commuter and parking space data, find the correlation coefficient, critical values for rrr, and test for significance at 0.05. 2. For CPI and subway fare, find the regression equation with CPI as xxx and predict fare for CPI = 182.5.

Problem 17

Explain kkk-fold cross-validation implementation and its pros/cons vs. validation set approach and LOOCV.

Problem 18

Test if the mean height of 5-year-olds is > 95 cm95 \mathrm{~cm}95 cm using a sample mean of 100 cm100 \mathrm{~cm}100 cm, n=20n=20n=20, σ=6 cm\sigma=6 \mathrm{~cm}σ=6 cm, at α=0.01\alpha=0.01α=0.01. a) State hypotheses, b) find test statistic, c) find P-value, d) make decision, e) conclude.

Problem 19

Problem 20

Problem 21

Problem 22

Find the zzz-score for a person who scored 616 on an exam with mean 500 and standard deviation 40.

Problem 23

Calculate the correlation coefficient between annual growth of National Income and Gross Domestic Saving from 1992-2002.

Problem 24

Conjecture the percentage of the population with type O blood from a sample result of 0.42. Is it descriptive or inferential statistics?

Problem 25

Students were surveyed on video game time and test averages. Is the correlation negative or weak? True/False statements provided.

Problem 26

Analyze the frequency table of art styles to determine if there's an association between art type and style.

Problem 27

A city inspector found that 41.1%41.1\%41.1% of 500 buildings met readiness conditions with a margin of error of ±5%\pm 5\%±5%. What must be true?

Problem 28

Find the confidence interval for the true mean SAT score given a mean of 482 and a margin of error of 15.

Problem 29

Which of these is a statistical question? A. Lunch period length? B. Oldest student age? C. Classrooms count? D. Ages of classmates?

Problem 30

Elise has two loans: a \$20,000 fixed-rate at 4.5\% and a \$20,000 variable-rate at 4.15\%. Which is more predictable in total cost?

Problem 31

Is the frequency distribution normal based on the criteria? Choose A, B, or C based on the given temperature ranges and frequencies.

Problem 32

Calculate the correlation coefficient rrr and the regression line for the given sea level pressure and wind speed data. Then predict wind speed for 977 millibars. Round appropriately.

Problem 33

Determine the correlation coefficient rrr, regression line, and predict weight for a 124-inch alligator. Is it valid for 20 inches?

Problem 34

Find the line of best fit for the data: (x,y)=(1,9.6),(2,6.3),(3,2.8),(4,8.73),(5,5.9),(6,1.2)(x, y) = (1, 9.6), (2, 6.3), (3, 2.8), (4, 8.73), (5, 5.9), (6, 1.2)(x,y)=(1,9.6),(2,6.3),(3,2.8),(4,8.73),(5,5.9),(6,1.2). Interpret the correlation coefficient.

Problem 35

Identify a Type II error from these options: rejecting H0H_0H0​ when H0H_0H0​ is false, true, or not rejecting when true/false.

Problem 36

What term describes findings in an experiment that reach conventional statistical significance? Options: nonsignificant, insignificant, significant, unworthy.

Problem 37

Is there a link between liking a TV show and viewer age? (a) Find expected adults who dislike: 20.1320.1320.13. (b) Calculate χ2\chi^{2}χ2 test statistic: χ2=∑(observed−expected)2expected\chi^{2}=\sum \frac{(observed - expected)^{2}}{expected}χ2=∑expected(observed−expected)2​.

Problem 38

Problem 39

Calculate expected values under the null hypothesis for party affiliation and support of full-body scans. (a) Expectation for Republicans not supporting: 484848 (b) Expectation for Democrats supporting: ??? (c) Expectation for Independents unsure: 222222

Problem 40

Analyze responses from 825 voters on oil drilling in CA. Perform a chi-square test for college grads vs non-grads at α=0.05\alpha = 0.05α=0.05. State hypotheses, calculate test statistic (2 decimal places), and find ppp-value (3 decimal places). Note data discrepancies.

Problem 41

Survey skiers' preferences for ski areas. Test if preference is independent of skill level at α=0.05\alpha=0.05α=0.05. Find test statistic and ppp-value.

Problem 42

A survey of 825 California voters examines opinions on offshore drilling. Perform a chi-square test with H0H_{0}H0​: no difference, HAH_{A}HA​: difference. Test statistic is 12.32; confirm and find the ppp-value.

Problem 43

True or false: For a population proportion confidence interval, we use $\mathrm{z}$ -distribution, not $\mathrm{t}$ -distribution.

Identify which statements about confidence intervals and distributions are true or false: 1) z vs t for population proportion, 2) degrees of freedom, 3) known $\sigma$ and Z, 4) unknown $\sigma$ and S, 5) t vs z for population proportion.

Find the test statistic $z$ for a sample mean of 84, size 49, standard deviation 14, testing if mean > 80 at $\alpha = 0.05$ .

Test if the mean score of sober subjects is 35 using scores: mean = 41, std dev = 3.7, n = 20, significance = 0.01.
Test if the proportion of women (65%) favoring gun control is higher than men (60%) using samples of 360 women and 220 men, significance = 0.05.

Commuters and parking spaces data: a) Find the correlation coefficient. b) Find critical values for $r$ . c) Check for significant correlation at 0.05 level. d) State the conclusion.
CPI and subway fare data: a) Find regression equation with CPI as $x$ . b) Predict subway fare for CPI = 182.5.

1. Given commuter and parking space data, find the correlation coefficient, critical values for $r$ , and check significance at 0.05.
2. For CPI and subway fare data, find the regression equation with CPI as $x$ and predict fare for CPI = 182.5.

Test if the mean score of sober subjects is 35 using a sample mean of 41, SD of 3.7, at 0.01 significance level.
Also, test if the proportion of women (65%) favoring stricter gun control is higher than men (60%) at 0.05 significance level.

How many people were unemployed in Africa in 2014 if the number is expected to reach 61 million in 2024, a $24.5 \%$ increase? Round to the nearest million.

Construct a confidence interval for garlic's effect on LDL cholesterol. Mean change: 3.2, SD: 18.6. Find point estimate and $95\%$ CI.

1. Given commuter and parking space data, find the correlation coefficient, critical values for $r$ , and test for significance at 0.05.
2. For CPI and subway fare, find the regression equation with CPI as $x$ and predict fare for CPI = 182.5.

Explain $k$ -fold cross-validation implementation and its pros/cons vs. validation set approach and LOOCV.

Test if the mean height of 5-year-olds is > $95 \mathrm{~cm}$ using a sample mean of $100 \mathrm{~cm}$ , $n=20$ , $\sigma=6 \mathrm{~cm}$ , at $\alpha=0.01$ . a) State hypotheses, b) find test statistic, c) find P-value, d) make decision, e) conclude.

Find the $z$ -score for a person who scored 616 on an exam with mean 500 and standard deviation 40.

A city inspector found that $41.1\%$ of 500 buildings met readiness conditions with a margin of error of $\pm 5\%$ . What must be true?

Calculate the correlation coefficient $r$ and the regression line for the given sea level pressure and wind speed data. Then predict wind speed for 977 millibars. Round appropriately.

Determine the correlation coefficient $r$ , regression line, and predict weight for a 124-inch alligator. Is it valid for 20 inches?

Find the line of best fit for the data: $(x, y) = (1, 9.6), (2, 6.3), (3, 2.8), (4, 8.73), (5, 5.9), (6, 1.2)$ . Interpret the correlation coefficient.

Identify a Type II error from these options: rejecting $H_0$ when $H_0$ is false, true, or not rejecting when true/false.

Is there a link between liking a TV show and viewer age? (a) Find expected adults who dislike: $20.13$ . (b) Calculate $\chi^{2}$ test statistic: $\chi^{2}=\sum \frac{(observed - expected)^{2}}{expected}$ .

Calculate expected values under the null hypothesis for party affiliation and support of full-body scans.
(a) Expectation for Republicans not supporting: $48$ (b) Expectation for Democrats supporting: $?$ (c) Expectation for Independents unsure: $22$

Analyze responses from 825 voters on oil drilling in CA. Perform a chi-square test for college grads vs non-grads at $\alpha = 0.05$ . State hypotheses, calculate test statistic (2 decimal places), and find $p$ -value (3 decimal places). Note data discrepancies.

Survey skiers' preferences for ski areas. Test if preference is independent of skill level at $\alpha=0.05$ . Find test statistic and $p$ -value.

A survey of 825 California voters examines opinions on offshore drilling. Perform a chi-square test with $H_{0}$ : no difference, $H_{A}$ : difference. Test statistic is 12.32; confirm and find the $p$ -value.

Test if skier level and preferred ski area are independent at $\alpha = 0.05$ . Calculate test statistic, p-value, and conclusions.

What type of statistics is it when $90 \%$ of taste testers prefer the new coffee brand? Options: Investigation, Description, Design, Inference, None.

Is the $31\%$ response from the poll a statistic or a parameter regarding voter opinions on immigration?

A historian finds marriage records from $1800-1820$ showing an average age of 26.7. Answer these questions about the data.

A historian estimates the average age at marriage of men (1800-1820): average age is 26.7 years, range is 25.8-27.6 years.
a. What summarizes the data? b. What infers about the population? c. What population is referred to? d. Is 26.7 a statistic or parameter?

Is $55\%$ of seniors owning a vehicle a statistic or a parameter? Choose the correct explanation.

Calculate the correlation coefficient $r$ , find the regression line, and predict the 5K time for $\mathrm{VO}_{2} \mathrm{max} = 24.79$ .

Analyze if hourly workers ( $31$ laid off) were more likely to be laid off than salaried ( $24$ laid off) using the data.

Estimate the number of employees out of 600 who read at least one book each month if $x$ out of 50 do.

A survey shows that of students living >1 mile, $76\%$ ride a bike. Which conclusion is best?

Valerie's team of 30 rated her as "outstanding" at $83\%$ . Why might this result be biased? Choose 1 answer: A, B, C, or D.

Use the Grubbs test to check if $0.1189$ is an outlier in the data set $0.1123, 0.1087, 0.1139, 0.1112, 0.1189$ at $95\%$ confidence. Show your calculations.

Tina's survey of 600 students shows $53\%$ exercise over 30 mins daily. Why is this misleading? Choose one: outlier, small sample, biased sample, calculation error.