Open Math Review for Exam 1

2.37 Portfolio return: A portfolio's value increases by 15% during a financial boom and by 9% during normal times. It decreases by 11% during a recession. What is the expected return on this portfolio if each scenario is equally likely?

(1/3)*(.15+.09-.11) = 4%

2.24 Exit poll: Edison Research gathered exit poll results from several sources for the Wisconsin recall election of Scott Walker. They found that 52% of the respondents voted in favor of Scott Walker. Additionally, they estimated that of those who did vote in favor for Scott Walker, 40% had a college degree, while 42% of those who voted against Scott Walker had a college degree. Suppose we randomly sampled a person who participated in the exit poll and found that he had a college degree. What is the probability that he voted in favor of Scott Walker?(please round to 4 decimal places)

(voted in favor and had a degree)/(total had a degree) = .5078

2.23 HIV in Swaziland: Swaziland has the highest HIV prevalence in the world: 25.9% of this country's population is infected with HIV. The ELISA test is one of the first and most accurate tests for HIV. For those who carry HIV, the ELISA test is 99.7% accurate. For those who do not carry HIV, the test is 92.6% accurate. If an individual from Swaziland has tested positive, what is the probability that he carries HIV?(please round to 4 decimal places)

.258223(+ and carries HIV)/ .313057(total +) = .8248

2.38 Baggage fees: An airline charges the following baggage fees: $25 for the first bag and $30 for the second. Suppose 49% of passengers have no checked luggage, 32% have only one piece of checked luggage and 19% have two pieces. We suppose a negligible portion of people check more than two bags. a) The average baggage-related revenue per passenger is: $ (please round to the nearest cent) b) The standard deviation of baggage-related revenue is: $ (please round to the nearest cent) c) About how much revenue should the airline expect for a flight of 130 passengers? $ (please round to the nearest dollar)

a) (.32*25) + (.19*55) = 18.45 b) sqrt[(-18.45^2*.49) + ((25-18.45)^2*.32) + ((55-18.45)^2*.19))] = 20.84 c) (130*18.45) = 2398.50

2.5 Coin Flips: If you flip a fair coin 8 times, what is the probability of each of the following?(please round all answers to 4 decimal places) a) getting all tails? b) getting all heads? c) getting at least one tails?

a) (1/2)(tails)^8(flips) = 0.0039 b)(1/2)(heads)^8(flips) = 0.0039 c) 1 - (1/2)^8 = 0.9960

1.1 Migraine and Acupuncture: A migraine is a particularly painful type of headache, which patients sometimes wish to treat with acupuncture. To determine whether acupuncture relieves migraine pain, researchers conducted a randomized controlled study where 90 females diagnosed with migraine headaches were randomly assigned to one of two groups: treatment or control. 45 patients in the treatment group received acupuncture that is specifically designed to treat migraines. 45 patients in the control group received placebo acupuncture (needle insertion at non-acupoint locations). 24 hours after patients received acupuncture, they were asked if they were pain free. Results are summarized in the contingency table below.(please round answers to within one hundredth of a percent) a) What percent of patients in the treatment group were pain free 24 hours after receiving acupuncture? b) What percent of patients in the control group were pain free after 24 hours? c) At first glance, does acupuncture appear to be an effective treatment for migraines? Explain your reasoning. d) Do the data provide convincing evidence that there is a real pain reduction for those patients in the treatment group? Or do you think that the observed difference might just be due to chance?

a) (10/45) = 22.22 b) (3/45) = 6.67 c) Yes, because a higher percentage of individuals in the treatment group were pain-free after 24 hours. d) It is impossible to tell merely by comparing the sample proportions because the difference could be the result of random error in our sample

2.10 Guessing on an exam: In a multiple choice exam, there are 6 questions and 4 choices for each question (a, b, c, d). Nancy has not studied for the exam at all and decides to randomly guess the answers. What is the probability that:(please round all answers to four decimal places) a) the first question she gets right is question number 5? b) she gets all of the questions right? c) she gets at least one question right?

a) (3/4)^4*(1/4) = .0791 b) (1/4)^6 = .0002 c) 1-(3/4)^6 = .8220

2.20 Assortative mating: Assortative mating is a nonrandom mating pattern where individuals with similar genotypes and/or phenotypes mate with one another more frequently than what would be expected under a random mating pattern. Researchers studying this topic collected data on eye colors of 215 Scandinavian men and their female partners. The table below summarizes the results (rows represent male eye color while columns represent female eye color). For simplicity, we only include heterosexual relationships in this exercise.(please round any numerical answers to 4 decimal places) Blue Brown Green Total Blue 47 20 28 95 Brown 18 22 15 55 Green 16 11 38 65 Total 81 53 81 215 a) What is the probability that a randomly chosen male respondent or his partner has blue eyes? b) What is the probability that a randomly chosen male respondent with blue eyes has a partner with blue eyes? c) What is the probability that a randomly chosen male respondent with brown eyes has a partner with blue eyes? d) What is the probability of a randomly chosen male respondent with green eyes having a partner with blue eyes? e) Does it appear that the eye colors of male respondents and their partners are independent? Explain.

a) (95+18+16) / 215 = .6000 b) (47/95) = .4947 c) (18/55) = .3273 d) (16/65) = .2462 e) No, it is much more likely for a male with blue eyes to have a blue-eyed partner than it is for a male with any other eye color

1.66 Views on immigration: 1200 randomly sampled registered voters from Tampa, FL were asked if they thought workers who have illegally entered the US should be (i) allowed to keep their jobs and apply for US citizenship, (ii) allowed to keep their jobs as temporary guest workers but not allowed to apply for US citizenship, or (iii) lose their jobs and have to leave the country. The results of the survey by political ideology are shown below.(Round all answers to the nearest hundredth of a percent) C M L Total AFC 57 123 229 409 GW 125 98 46 269 LTC 174 108 35 317 NS 104 31 70 205 Total 460 360 380 1200 a) What percent of these Tampa, FL voters identify themselves as conservatives? Correct % b) What percent of these Tampa, FL voters are in favor of the citizenship option? Correct % c) What percent of these Tampa, FL voters identify themselves as conservative and are in favor of the citizenship option? d) What percent of these Tampa, FL voters who identify themselves as conservatives are also in favor of the citizenship option? e) What percent of moderates share this view (favor the citizenship option)? f) What percent of liberals share the view (favor the citizenship option)? g) Political ideology and views on immigration appear to be:

a) (total conservative) / (total voters) = 38.3 b) (total apply for citizenship) / (total voters) = 34.1 c) (conservative and apply for citizenship) / (total voters) = 4.8 d) (conservative and apply for citizenship) / (total conservative) 12.4 e) (moderate and apply for citizenship) / (total moderate) = 34.2 f) (liberal and apply for citizenship) / (total liberal) = 60.3 g) dependent

2.33 College smokers: At a university, 14% of students smoke. a) Calculate the expected number of smokers in a random sample of 180 students from this university (please do not round your answer) b) The university gym opens at 9 am on Saturday mornings. One Saturday morning at 8:55 am there are 25 students outside the gym waiting for it to open. Should you use the same approach from part (a) to calculate the expected number of smokers among these 25 students?

a) .14*180 = 25.2 b) No, it is unlikely that smoking habits and waking up early to go to the gym on Saturday are independent

2.6 Dice Rolls: If you roll a pair of fair dice, what is the probability of each of the following? (round all answers to 4 decimal places) a) getting a sum of 1? b) getting a sum of 5? c) getting a sum of 12?

a) 0.0000 minimum = 2 b) 4(combinations)/36(6^2) = 0.1111 c) 1(combinations)/36(6^2) = 0.0278

2.2 Roulette wheel: The game of roulette involves spinning a wheel with 38 slots: 18 red, 18 black, and 2 green. A ball is spun onto the wheel and will eventually land in a slot, where each slot has an equal chance of capturing the ball. a) You watch a roulette wheel spin 4 consecutive times and the ball lands on a red slot each time. What is the probability that the ball will land on a red slot on the next spin? (please round to four decimal places) b) You watch a roulette wheel spin 210 consecutive times and the ball lands on a red slot each time. What is the probability that the ball will land on a red slot on the next spin? (please round to four decimal places)

a) 18(red)/38(total slots) = .4737 b) 18(red)/38(total slots) = .4737

2.36 Is it worth it?: Andy is always looking for ways to make money fast. Lately, he has been trying to make money by gambling. Here is the game he is considering playing: The game costs $2 to play. He draws a card from a deck. If he gets a number card (2-10), he wins nothing. For any face card ( jack, queen or king), he wins $3. For any ace, he wins $5, and he wins an extra $20 if he draws the ace of clubs. a) Andy's expected profit per game is: $ (round to the nearest cent) b) Would you recommend this game to Andy as a good way to make money? Explain.

a) 2 - [P(Num) + P(JQK) + P(A) + P(A|C)] = -0.54 b) No, we expect Andy to lose money each time he plays this game

1.46/47 Means, Medians, Standard Deviations, and IQRs: Answer the following about each dataset. (Round to two decimal places where appropriate) Dataset I: 1 2 3 4 5 a) The median of Dataset I is b) The IQR of Dataset I is c) The mean of Dataset I is d) The standard deviation of Dataset I is Dataset II: 6 7 8 9 10 e) The median of Dataset II is f) The IQR of Dataset II is g) The mean of Dataset II is h) The standard deviation of Dataset II is

a) 3 b) 1.5 to 4.5 c) 3 d) 1.58 e) 8 f) 6.5 to 9.5 g) 8 h) 1.58

2.44 Cat weights: The histogram shown below represents the weights (in kg) of 47 female and 97 male cats. Just read the histogram and add values a) Approximately % of these cats weigh less than 2.5kg. b) Approximately % of these cats weigh between 2.5 and 2.75kg. c) Approximately % of these cats weigh between 2.75 and 3.5kg.

a) 43% b) 18% c) 30%

1.42 Sleeping in college: A recent article in a college newspaper stated that college students get an average of 6.4 hrs of sleep each night. A student who was skeptical about this value decided to conduct a survey by randomly sampling 32 students. On average, the sampled students slept 5.2 hours per night. Identify which value represents the sample mean and which value represents the claimed population mean. a) What is the sample mean? ______ hours b) What is the claimed population mean? ______ hours

a) 5.2 b) 6.4

1.46/47 Means, Medians, Standard Deviations, and IQRs: Answer the following about each dataset. (Round to two decimal places where appropriate) Dataset I: 0 10 50 60 100 a) The median of Dataset I is b) The IQR of Dataset I is c) The mean of Dataset I is d) The standard deviation of Dataset I is Dataset II: 0 100 500 600 1000 e) The median of Dataset II is f) The IQR of Dataset II is g) The mean of Dataset II is h) The standard deviation of Dataset II is

a) 50 b) 5 to 80 c) 44 d) 40.37 e) 500 f) 50 to 800 g) 440 h) 403.73

1.43 Parameters and statistics: Identify which value represents the sample mean and which value represents the claimed population mean. a) American households spent an average of about $72 in 2007 on Halloween merchandise such as costumes, decorations and candy. To see if this number had changed, researchers conducted a new survey in 2008 before industry numbers were reported. The survey included 2350 households and found that average Halloween spending was $57 per household. The sample mean is ______ dollars, while the claimed population mean is _______ dollars. b) The average GPA of students in 2001 at a private university was 3.59. A survey on a sample of 240 students from this university yielded an average GPA of 3.51 in Spring semester of 2012.The sample mean is ________ and the claimed population mean is __________

a) 57, 72 b) 3.51, 3.59

1.46/47 Means, Medians, Standard Deviations, and IQRs: Answer the following about each dataset. (Round to two decimal places where appropriate) Dataset I: 3 5 6 7 9 a) The median of Dataset I is b) The IQR of Dataset I is c) The mean of Dataset I is d) The standard deviation of Dataset I is Dataset II: 3 5 6 7 20 e) The median of Dataset II is f) The IQR of Dataset II is g) The mean of Dataset II is h) The standard deviation of Dataset II is

a) 6 b) 4 to 8 c) 6 d) 2.24 e) 6 f) 4 to 13.5 g) 8.2 h) 6.76

1.46/47 Means, Medians, Standard Deviations, and IQRs: Answer the following about each dataset. (Round to two decimal places where appropriate) Dataset I: 3 5 6 7 9 a) The median of Dataset I is b) The IQR of Dataset I is c) The mean of Dataset I is d) The standard deviation of Dataset I is Dataset II: 3 5 8 7 9 e) The median of Dataset II is f) The IQR of Dataset II is g) The mean of Dataset II is h) The standard deviation of Dataset II is

a) 6 b) 4 to 8 c) 6 d) 2.24 e) 7 f) 4 to 8.5 g) 6.4 h) 2.4

1.10 Cheaters, scope of inference: Exercise 1.5 introduces a study where researchers studying the relationship between honesty, age, and self-control conducted an experiment on 160 children between the ages of 5 and 15. The researchers asked each child to toss a fair coin in private and to record the outcome (white or black) on a paper sheet, and said they would only reward children who report white. Half the students were explicitly told not to cheat and the others were not given any explicit instructions. Differences were observed in the cheating rates in the instruction and no instruction groups, as well as some differences across children's characteristics within each group. a) Identify the population of interest in the study. b) Identify the sample for this study. c) Can the results of the study can be generalized to the population? Should the findings of the study can be used to establish causal relationships.

a) All children between the ages of 5 and 15 b) 160 children between the ages of 5 and 15 c) If the sample is randomly selected and representative of the entire population, then the results can be generalized to the target population. Furthermore, since this study is experimental, the findings can be used to infer causal relationships.

1.12 Stealers, scope of inference: Exercise 1.6 introduces a study on the relationship between socio-economic class and unethical behavior. As part of this study 129 University of California Berkeley undergraduates were asked to identify themselves as having low or high social-class by comparing themselves to others with the most (least) money, most (least) education, and most (least) respected jobs. They were also presented with a jar of individually wrapped candies and informed that the candies were for children in a nearby laboratory, but that they could take some if they wanted. After completing some unrelated tasks, participants reported the number of candies they had taken. It was found that those who were identified as upper-class took more candy than others. a) Identify the population of interest in the study. b) Identify the sample in this study. c) Can the results of the study can be generalized to the population? d) Can the findings of the study be used to establish causal relationships?

a) all UC Berkeley undergraduates b) the 129 UC Berkeley undergraduates c) It depends. If the sample is randomly selected and representative of the entire population, then the results can be generalized to the target population. d) Since this study is observational, the results cannot be used to infer causal relationships.

1.11 Buteyko method, scope of inference: Exercise 1.4 introduces a study on using the Buteyko shallow breathing technique to reduce asthma symptoms and improve quality of life. As part of this study 600 asthma patients aged 18-69 who relied on medication for asthma treatment were recruited and randomly assigned to two groups: one practiced the Buteyko method and the other did not. Those in the Buteyko group experienced, on average, a significant reduction in asthma symptoms and an improvement in quality of life. a) Identify the population of interest in the study. b) Identify the sample in this study. c) Can the results of the study can be generalized to the population? d) Can the findings of the study be used to establish causal relationships?

a) all asthma patients aged 18-69 who rely on medication for asthma treatment b) the 600 asthma patients aged 18-69 who rely on medication for asthma treatment c) It depends. If the sample is randomly selected and representative of the entire population, then the results can be generalized to the target population. d) Since this study is experimental, the findings can be used to infer causal relationships.

1.8 Smoking habits of UK residents: A survey was conducted to study the smoking habits of UK residents. Below is a data matrix displaying a portion of the data collected in this survey. Note that "£" stands for British Pounds Sterling, "cig" stands for cigarettes, and "N/A" refers to a missing component of the data. Look at data chart a) What does each row of the data matrix represent? b) How many participants were included in the survey?Correct c) Identify each variable, determine whether each variable is numerical or categorical. If the variable is numerical, specify continuous or discrete. If the variable is categorical, specify whether the variable is ordinal or not.

a) an observation b) 1980 c) The variables are sex (regular categorical), age (discrete), marital status (regular categorical), earnings (ordinal), whether or not the individual smokes (regular categorical), amount the individual smokes per day on a weekday (discrete), amount the individual smokes per day on a weekend (discrete)

1.44 Make-up exam: In a class of 24 students, 23 of them took an exam in class and 1 student took a make-up exam the following day. The professor graded the first batch of 23 exams and found an average score of 78 points with a standard deviation of 5.8 points. The student who took the make-up the following day scored 62 points on the exam. a) Does the new student's score increase or decrease the average? b) The new average is: ____ (round to two decimal places) c) Does the new student's score increase or decrease the standard deviation of the scores?

a) decreases b) ((78*23)+62)/24 = 77.33 c) increases

1.31 Light and exam performance: A study is designed to test the e↵ect of light level on exam performance of students. The researcher believes that light levels might have different effects on males and females, so wants to make sure both are equally represented in each treatment. The treatments are fluorescent overhead lighting, yellow overhead lighting, no overhead lighting (only desk lamps). a) What is the response variable? b) What is the explanatory variable? c) What is the blocking variable?

a) exam performance b) light level c) sex

1.32 Vitamin supplements: In order to assess the effectiveness of taking large doses of vitamin C in reducing the duration of the common cold, researchers recruited 400 healthy volunteers from staff and students at a university. A quarter of the patients were assigned a placebo, and the rest were evenly divided between 1g Vitamin C, 3g Vitamin C, or 3g Vitamin C plus additives to be taken at onset of a cold for the following two days. All tablets had identical appearance and packaging. The nurses who handed the prescribed pills to the patients knew which patient received which treatment, but the researchers assessing the patients when they were sick did not. No significant differences were observed in any measure of cold duration or severity between the four medication groups, and the placebo group had the shortest duration of symptoms a) Was this an experiment or observational study? b) What is the explanatory variable? c) What is the response variable? d) Were the patients blind to their treatment? e) Was the study double-blind?

a) experiment b) level of vitamin C supplement c) duration of cold d) Yes e) No

2.9 Disjoint vs. independent: In parts (a) and (b), identify whether the events are disjoint, independent, or neither (events cannot be both disjoint and independent). a) You and a randomly selected student from your class both earn A's in this course. b) You and your class partner both earn A's in this course. c) If two events can occur at the same time, they must be independent.

a) independent b) neither c) false

2.11 Educational attainment of couples: The table below shows the distribution of education level attained by US residents by gender based on data collected during the 2010 American Community Survey. (please round all answers to four decimal places) A B C D F a 0.3 0.3 0.3 0.2 0.1 b 0 0 1 0 0 c 0.3 0.3 0.3 0 0 d 0.3 0.5 0.2 0.1 -0.1 e 0.2 0.4 0.2 0.1 0.1 f 0 -0.1 1.1. 0 0 a) Distribution (a) is a/an: b) Distribution (b) is a/an: c) Distribution (c) is a/an: d) Distribution (d) is a/an: e) Distribution (e) is a/an: f) Distribution (f) is a/an:

a) invalid probability distribution b) valid probability distribution c) invalid probability distribution d) invalid probability distribution e) valid probability distribution f) invalid probability distribution

2.17 Global warming: A research poll asked 1499 Americans "From what you've read and heard, is there solid evidence that the average temperature on earth has been getting warmer over the past few decades, or not?". The table below shows the distribution of responses by party and ideology, where the counts have been replaced with relative frequencies. EW NW DK Total CR 0.06 0.17 0.02 0.25 M/L R 0.12 0.04 0.03 0.19 M/C D 0.13 0.03 0.02 0.18 LD 0.30 0.00 0.08 0.38 Total 0.61 0.24 0.15 1 a) Are believing that the earth is warming and being a liberal Democrat mutually exclusive? b) What is the probability that a randomly chosen respondent believes the earth is warming or is a liberal Democrat? c) What is the probability that a randomly chosen respondent believes the earth is warming given that they are a liberal Democrat? d) What is the probability that a randomly chosen respondent believes the earth is warming given that they are a conservative Republican? e) Does it appear that whether or not a respondent believes the earth is warming is independent of their party ideology? f) What is the probability that a randomly chosen respondent is a moderate/liberal Republican given that they do not believe that the earth is warming?

a) not mutually exclusive b) (.61+.38-.30) = .6900 EW+LD-(LD and EW) c) (.30/.38) = .7895 (LD and EW)/LD d) (.06/.25) = .2400 (CR and EW)/CR e) belief in global warming and party ideology are dependent f) (.04/.24) = .1667 (MLR and NW)/(NW)

1.15 GPA and study hours: A survey was conducted on 193 Duke University undergraduates who took an introductory statistics course in 2012. Among many other questions, this survey asked them about their GPA, which can range between 0 and 4 points, and the number of hours they spent studying per week. The scatterplot below displays the relationship between these two variables. scattered from bottom left to top right and above x-axis - study hours/week y-axis - GPA a) What is the explanatory variable? b) What is the response variable? c) Describe the relationship between the variables. d) Is this an experiment or an observational study? e) Can we conclude that studying longer hours leads to higher GPAs?

a) number of study hours per week b) GPA c) weak positive d) observational study e) No

1.13 Relaxing after work: The 2010 General Social Survey asked the question, "After an average work day, about how many hours do you have to relax or pursue activities that you enjoy?" to a random sample of 1,155 Americans. The average relaxing time was found to be 1.65 hours. Determine which of the following is an observation, a variable, a sample statistic, or a population parameter. a) An American in the sample. b) Number of hours spent relaxing after an average work day. c) 1.65. d) Average number of hours all Americans spend relaxing after an average work day.

a) observation b) variable c) sample statistic d) population parameter

1.16 Income and education in US counties: The scatterplot below shows the relationship between per capita income (in thousands of dollars) and percent of population with a bachelor's degree in 3,143 counties in the US in 2010. scattered heavily at bottom left but grows to top right with less scattering a) What is the explanatory variable? b) What is the response variable? c) Describe the relationship between the variables. d) Can we conclude that having a bachelor's degree increases one's income?

a) percent with a bachelor's degree b) per capita income (in $1000s) c) strong positive d) No

1.14 Cats on YouTube: Suppose you want to estimate the percentage of videos on YouTube that are cat videos. It is impossible for you to watch all videos on YouTube so you use a random video picker to select 1000 videos for you. You find that 2% of these videos are cat videos. Determine which of the following is an observation, a variable, a sample statistic, or a population parameter. a) The percentage of all videos on YouTube that are cat videos is a/an: b) 2% c) A video in your sample d) Whether or not a video is a cat video

a) population parameter b) sample statistic c) observation d) variable

1.39 Associations: Describe the relationship between the predictor and response variables in each of the four scatterplots below. (1) diagonal scattered bottom left to top right (2) scattered over whole graph (3) exponential from bottom left to top right, right portion half U (4) diagonal scattered top left to bottom right a) Describe plot (1) above: b) Describe plot (2) above: c) Describe plot (3) above: d) Describe plot (4) above:

a) positive, linear b) no association c) positive, non-linear d) negative, linear

1.56 Distributions and appropriate statistics (Part II): For each of the following, state whether you expect the distribution to be symmetric, right skewed, or left skewed. Also specify whether the mean or median would best represent a typical observation in the data, and whether the variability of observations would be best represented using the standard deviation or IQR. Explain your reasoning.(a) Housing prices in a country where 25% of the houses cost below $350,000, 50% of the houses cost below $450,000, 75% of the houses cost below $1,000,000 and there are a meaningful number of houses that cost more than $6,000,000. a) The distribution is expected to be: A typical observation is best represented by the: The variability in the observations is best measured by the: (b) Housing prices in a country where 25% of the houses cost below $300,000, 50% of the houses cost below $600,000, 75% of the houses cost below $900,000 and very few houses that cost more than $1,200,000. The distribution is expected to be: A typical observation is best represented by the: The variability in the observations is best measured by the: (c) Number of alcoholic drinks consumed by college students in a given week. Assume that most of these students don't drink since they are under 21 years old, and only a few drink excessively. The distribution is expected to be: A typical observation is best represented by the: The variability in the observations is best measured by the: (d) Annual salaries of the employees at a Fortune 500 company where only a few high level executives earn much higher salaries than the all other employees. The distribution is expected to be: A typical observation is best represented by the: The variability in the observations is best measured by the:

a) right skewed median IQR b) symmetric mean standard deviation c) right skewed median IQR d) right skewed median IQR

1.5 Cheaters, study components: Researchers studying the relationship between honesty, age, and self-control conducted an experiment on 160 children between the ages of 5 and 15. Participants reported their age, sex, and whether they were an only child or not. The researchers asked each child to toss a fair coin in private and to record the outcome (white or black) on a paper sheet, and said they would only reward children who report white. Half the students were explicitly told not to cheat and the others were not given any explicit instructions. In the "no instruction" group the probability of cheating was found to be uniform across groups based on a child's characteristics. In the group that was explicitly told to not cheat, girls were less likely to cheat, and while rate of cheating didn't vary by age for boys, it decreased with age for girls (Ritz et al. 2000). Identify the following a) What are the cases? b) What are the variables and their types? c) What is the main research question?

a) the 160 children between the ages of 5 and 15 b) The variables and types are age (discrete), sex (regular categorical), whether they were an only child or not (regular categorical), the result of the coin flip (regular categorical), whether the children were given instructions or not (regular categorical), and whether the child cheated (regular categorical) c) What is the effect of age, sex, only child status, and whether or not children were given instructions on the rate of cheating in a game?

1.67 Views on the DREAM Act: A random sample of registered voters from Tampa, FL were asked if they support the DREAM Act, a proposed law which would provide a path to citizenship for people brought illegally to the US as children. The survey also collected information on the political ideology of the respondents. Based on the mosaic plot shown below, do views on the DREAM Act and political ideology appear to be independent? Explain your reasoning. Look at the mosaic plot Views on the DREAM Act and political affiliation appear to be: Explain your reasoning:

dependent From the mosaic plot, it looks as though a higher proportion of liberals support the DREAM Act

1.68 Raise Taxes: A random sample of registered voters nationally were asked whether they think it's better to raise taxes on the rich or raise taxes on the poor. The survey also collected information on the political party affiliation of the respondents. Based on the mosaic plot shown below, do views on raising taxes and political affiliation appear to be independent? Explain your reasoning. Look at the mosaic plot Views on raising taxes and political affiliation appear to be: Explain your reasoning:

dependent From the mosaic plot, it looks as though a larger proportion of Democrats think it is better to raise taxes on the rich