Chapter P.1 Exercise Question 10 P.1.10 In August of 2005, researchers for the American Society for Microbiology and the Soap and Detergent Association monitored the behavior of more than 6,300 users of public restrooms. They observed people in public venues such as Turner Field in Atlanta and Grand Central Station in New York City. For each person they kept track of the person's sex and whether or not the person washed his or her hands along with the person's location. Which of the following are the variables recorded on each observational units? gender, washed hands, and public restroom users gender and location only washed hands, location, and public restroom users gender, washed hands, and location Based on the graph, are women more likely to wash their hands after using the restroom than men? yes Chapter P.1 Exercise Question 15 P.1.15 Suppose that the observational units in a statistical study are purchases made on a particular website (think of amazon.com) for one month. no Which of the following are categorical variables that could be recorded for these purchases? Select all that apply. whether or not they purchased a particular item purchaser's gender whether or not they viewed a particular item price of items purchased shipping costs for items purchased purchaser's age Which of the following are quantitative variables that could be recorded for these purchases? Select all that apply. price of items purchased purchaser's age shipping costs for items purchased purchaser's gender the state to which the purchase is being shipped product types purchased Chapter P.2 Exercise Question 06 P.2.6 In the 2012 National Football League (NFL) season, the first three weeks' games were played with replacement referees because of a labor dispute between the NFL and its regular referees. Many fans and players were concerned with the quality of the replacement referees' performance. We could examine whether data might reveal any differences between the three weeks' games played with replacement referees and the next three weeks' games that were played with regular referees. The pair of dotplots shown display data on the total number of penalties called in the game, again separated by the type of referee. Select all the statements below which might reveal whether the two types of referees differ with regard to the distributions of this variable. The number of penalties assessed by regular referees seems to be higher than the number of penalties assessed by replacement referees. The game that had the highest number of penalties assessed was officiated by a regular referee. Both distributions are fairly symmetric, centered around 12 penalties, with a minimum of 4 penalties and a maximum of 24-25 penalties. The games with 23-25 penalties are a bit unusual for both types of referees, with a few more of these extreme games for the replacement referees. Chapter P.3 Exercise Question 04 P.3.4 Answer this question for each of the following statements: Which of the following explains what it means to say \"the probability of ...\" while describing the random process that is repeated over and over again? The probability of getting a red M&M candy is 0.2. If you repeatedly draw M&Ms at random a very large number of times, in the long-run 20% of those M&Ms will be red. Each time you draw ten M&Ms, two of the M&Ms should be red. For every 100 M&Ms, there should be 20 M&Ms in the bag of candies. All of these are correct interpretations of probability. The probability of winning at a \"daily number\" lottery game is 1/1000. If 1000 people play the lottery, exactly one of those playing will win the lottery. Each time the lottery is played, one of 1000 people playing will win. If you repeatedly play the lottery a very large number of times, in the long run, you will win 0.1% of the times you play. All of these are correct interpretations of probability. The probability of rain tomorrow is 0.3. Thirty percent of the region will receive rain tomorrow. If you repeatedly record whether or not it rains for a large number of days with the same weather conditions as tomorrow, in the long run you will see rain on 30% of such days. Residents of the city should prepare for about 7.2 hours (30% of 24 hours) of rain on the next day. None of these are correct. Pennies can be a nuisance. Suppose 30% of the population of adult Americans want to get rid of the penny. If I randomly select one person from this population, the probability this person wants to get rid of the penny is 0.30. If you repeatedly select an adult American at random a large number of times, in the long run, roughly 30% of the time the selected adult will vote to get rid of the penny. If you ask 10 people if they are in favor of getting rid of the penny, 3 of them will say yes. There are 30 out of every 100 people who would agree that they would vote to get rid of the penny. All of these are correct. Suppose a polling organization takes a random sample of 100 people from the population of adults in a city, (where 30% of this population wants to get rid of the penny). Then the probability is 0.015 that the sample proportion who want to get rid of the penny is less than 0.20. Stating, "If you repeatedly select a sample of 100 adults from this city and record the proportion that want to get rid of the penny for each sample, in the long run roughly 1.5% of these samples will have at most 20% of the sample wanting to get rid of the penny," would explain what it means to say "the probability of ..." while describing the random process that is repeated over and over again. True False Chapter P.3 Exercise Question 06 P.3.6 Suppose that baseball team A is better than baseball team B. Team A is enough better that it has a 2/3 probability of beating team B in any one game, and this probability remains the same for each game, regardless of the outcomes of previous games. Suppose that team A and team B play a best-of-three series, meaning that the first team to win two games wins the series. If you are a fan of team A, would it be preferable to play a single game or a best-of-three series, or is there no difference? It would be preferable for team A to play a single game, because they can play their best pitcher and probably win. It doesn't matter whether they play a single game or a best-of-three series. They should win anyway with the large probability. It would be preferable for team A to play the best-of-three series, because in the longer series there is less of a chance for a weaker team to achieve the upset win multiple times. Which of the following describes how a six-sided die could be used to simulate one repetition of a best-ofthree series between teams A and B? Let rolls 1, 2, and 3 represent team A winning a game and 4, 5, and 6 represent team B winning a game. Roll the die and record who wins the game until one team has won two games (two or three times). Let rolls 1 and 2 represent team B winning a game and 3-6 represent team A. Roll the die and record who wins the game until one team has won two games (two or three times). Let rolls 1 and 2 represent team A winning a game and 3-6 represent team B. Roll the die and record who wins the game until one team has won two games (two or three times). There is not a preferred method of the three listed. Of the methods listed below, select which would be the best use of a six-sided die to approximate the probability that team A would win the best-of-three series against team B. Let rolls 1 and 2 represent team A winning a game and 3-6 represent team B. Roll the die and record who wins the game until one team has won two games (two or three times). Repeat the simulation for 100 times and record how often team A wins divided by the number of repetitions. Let rolls 1, 2, and 3 represent team A winning a game and 4, 5, and 6 represent team B winning a game. Roll the die and record who wins the game until one team has won two games (two or three times). Repeat the simulation 50 times and record how often team A wins divided by the number of repetitions. Let rolls 1 and 2 represent team B winning a game and 3-6 represent team A. Roll the die and record who wins the game until one team has won two games (two or three times). Repeat the simulation a large number of times (say 1000) and record how often team A wins divided by the number of repetitions. There is not a preferred method of the three listed. It turns out that the probability is 0.741 that team A would win this best-of-three series against team B. What does this probability mean? Select all that apply. If teams A and B repeatedly play a best-of-three series, then in the long run team A will win 74.1% of those Team A has a higher chance of winning the best of three series than the 2/3 chance of winning any one game). All of these statements are correct. None of these statements are correct. If teams A and B play a best-of-three series for 1000 times, then team A will win 741 of those series. Chapter 01.1 Exercise Question 05 1.1.5 LeBron James of the Miami Heat hit 765 of his 1354 field goal attempts in the 2012/2013 season for a shooting percentage of 56.5%. Over the lifetime of LeBron's career, can we say he is more likely than not to make a field goal? Describe the parameter of interest. LeBron's long-run proportion of making a field goal the proportion of shots LeBron made in the 2012/2013 season the proportion of all shots made by NBA players in LeBron's career the number of shots LeBron made in the 2012/2013 season What statistical term is given to the value 56.5%? statisti c paramete r sampl e chance model What value would the chance model assign to LeBron's long-run proportion of making a field goal? 56.5% 25% 765 50% Describe how to use coin flipping to simulate the 2012/2013 season under the assumption of the chance model. Flip a coin 1000 times and record the number of heads. Repeat this process 765 times. Flip a coin 1354 times and record the number of heads. This number represents the long-run proportion. Flip a coin 1354 times and record the number of heads. Repeat this 1000 times, keeping track of the number of heads in each set of 1354. Flip a coin 765 times and record the number of heads. Multiply this value by 1354. Suppose coin flipping was used to simulate the 2012/2013 season under the assumption of the chance model. What would be a typical number of heads recorded from a repetition of 1354 coin flips? Nothing can be known about the typical number of heads without doing the simulation. LeBron James is a great player so we can assume he will make at least 60% of his shots. Approximately of 1354 (677) will be one of the most likely values since we assume the chance model is true. 56.5% of 1354 (765) will be one of the most likely values since we assume the chance model is true and the chance probability is 56.5%. Chapter 01.2 Exercise Question 13 1.2.13 Hope the dog Suppose you are testing to see if your dog, Hope, understands pointing towards an object. You put Hope through 20 trials and 12 times (or 60%) she goes to the correct object when given a choice between two objects. You then conduct a test of significance and generate the following 100 simulations using an applet. Probability of heads: 0.5 Number of tosses: 20 Number of repetitions: 100 Total = 100 Which of the following explains the null and alternative hypotheses? Null: The long-run proportion of times Hope will go to the correct object is 0.50, Alt: The long-run proportion of times that Hope will go to the correct object is less than 0.50 Null: The long-run proportion of times Hope will go to the correct object is 0.50, Alt: The long-run proportion of times that Hope will go to the correct object is more than 0.50 Null: The long-run proportion of times Hope will go to the incorrect object is 0.50, Alt: The long-run proportion of times that Hope will go to the correct object is less than 0.50 Null: The long-run proportion of times Hope will go to the correct object is 0.50, Alt: The long-run proportion of times that Hope will go to the incorrect object is more than 0.50 represent the null and alternative hypotheses in symbols. Which is the most valid p-value? 2.3 (23 dots are 0.60 or larger) 0.023 (23 dots are 0.60 or smaller) 0.32 (23 dots are 0.60 or larger) 0.23 (23 dots are 0.60 or larger) Does the p-value indicate strong evidence that Hope understands pointing? Yes, the approximate p-value is 0.23, which provides evidence that Hope understands pointing. Yes, the approximate p-value is 0.23, which provides evidence that Hope understands pointing. No, the approximate p-value is 0.23, which provides little to no evidence that Hope understands pointing. No, the approximate p-value is 2.3, which provides little to no evidence that Hope understands pointing. What is the smallest proportion of times Hope could go toward the correct object so that you would have strong evidence that Hope understands pointing towards an object? 0.60 0.50 0.70 0.80 Which of the following best describes what a single dot represents in the null distribution shown? one possible value of the proportion of times Hope goes to the incorrect object out of 20 if she goes to the incorrect object 50% of the time in the long run one possible value of the proportion of times Hope goes to the correct object out of 20 if she goes to the correct object more than 50% of the time in the long run one possible value of the proportion of times Hope goes to the correct object out of 20 if she goes to the correct object 50% of the time in the long run one possible value of the proportion of times Hope goes to the correct object out of 20 if she goes to the correct object less than 50% of the time in the long run Chapter 01.2 Exercise Question 22 1.2.22 Spinning a coin It has been stated that spinning a coin on a table will result in it landing heads side up fewer than 50% of the time in the long run. One of the authors tested this by spinning a penny 50 times on a table and it landed heads side up 21 times. A test of significance was then conducted with the following hypotheses: H0: = 0.50, Ha: < 0.50. The symbol in this context stands for the long-run proportion of the time that a spun penny lands on Use an applet to conduct a simulation with at least 1000 repetitions. Which p-value is the most valid? The p-value is 0.16; there is little to no evidence that a spun penny lands heads up less than 50% of the time. The p-value is 0.56; there is little to no evidence that a spun penny lands tails up less than 50% of the time. The p-value is 0.016; there is strong evidence that a spun penny lands heads up more than 50% of the time. The p-value is 0.84; there is little to no evidence that a spun penny lands tails up less than 50% of the time. Suppose you focused on the proportion of times the coin landed tails up instead of heads up. How would your hypotheses be different? What would you do differently to calculate your p-value? Null would be < 0.5, alternative would be < 0.5. To calculate the p-value, find the probability that 29 or larger (58% or smaller) occurred. Null would be the same, alternative would be < 0.5. To calculate the p-value, find the probability that 29 or smaller (58% or smaller) occurred. Null would be the same, alternative would be = 0.5. To calculate the p-value, find the probability that 29 or smaller (58% or smaller) occurred. Null would be the same, alternative would be > 0.5. To calculate the p-value, find the probability that 29 or larger (58% or larger) occurred. Chapter 01.3 Exercise Question 13 1.3.13 Right or left Most people are right-handed, and even the right eye is dominant for most people. Molecular biologists have suggested that late-stage human embryos tend to turn their heads to the right. In a study reported in Nature (2003), German bio-psychologist OnurGntrkn conjectured that this tendency to turn to the right manifests itself in other ways as well, so he studied kissing couples to see which side they tended to lean their heads while kissing. He and his researchers observed kissing couples in public places such as airports, train stations, beaches, and parks. They were careful not to include couples who were holding objects such as luggage that might have affected which direction they turned. For each kissing couple observed, the researchers noted whether the couple leaned their heads to the right or to the left. They observed 124 couples, ages 13-70 years. Suppose that we want to use the data from this study to investigate whether kissing couples tend to lean their heads right more often than would happen by random chance. The symbol represents the long-run proportion of all the couples that lean their heads while kissing. Which of the following best describes the null hypothesis and the alternative hypothesis using ? null: 0.5, alternative: < 0.5 null: = 0.5, alternative: > 0.5 null: = 0.5, alternative: < 0.5 null: 0.5, alternative: > 0.5 Of the 124 kissing couples, 80 were observed to lean their heads right. What is the observed proportion of kissing couples who leaned their heads to the right? What symbol should you use to represent this value? (Round answer to 3 decimal places, e.g. 5.275) p^= the absolute tolerance is +/-0.001 Determine the standardized statistic from the data. (Hint: You will need to get the standard deviation of the simulated statistics from the null distribution.) (Round answer to 2 decimal places, e.g. 52.75) z= the absolute tolerance is +/-0.02 Interpret the meaning of the standardized statistic. The observed proportion of couples who leaned to the right when kissing is 3.22 standard deviations above the null hypothesized value of 0.50. The observed proportion of couples who leaned to the right when kissing is 3.22 standard deviations below the null hypothesized value of 0.50. The observed proportion of couples who leaned to the right when kissing is 3.22 standard deviations away from the null hypothesized value of 0.50. Select the best conclusion that you would draw about the null and alternate hypotheses. We have strong evidence that the proportion of couples that lean their heads to the right while kissing is less than 50%. We have strong evidence that the proportion of couples that lean their heads to the right while kissing is near to 50%. We have strong evidence that the proportion of couples that lean their heads to the right while kissing is more than 50%. We have strong evidence that the proportion of couples that lean their heads to the right while kissing is 50%. Chapter 01.3 Exercise Question 22 1.3.22 Choosing numbers Use the following information to answer the next questions. It has been conjectured that when people are asked to choose a number from the choices 1, 2, 3, and 4, they tend to choose \"3\" more than would be expected by random chance. To investigate this, a professor collected data in her class. Here is the table of responses from her students: What is the parameter of interest in the context of the study using symbol ? The long-run proportion of people that choose the number 1 The long-run proportion of people that choose the number 2 The long-run proportion of people that choose the number 4 The long-run proportion of people that choose the number 3 Which of the following best describes the null hypothesis and the alternative hypothesis using the appropriate symbol? null: p^=0.25, alternative: p^<0.25 null: =0.25, alternative: >0.25 null: p^=0.25 , alternative: p^>0.25 null: =0.25, alternative: <0.25 What is the observed proportion of times students chose the number 3? What symbol should you use to represent this value? (Round answer to 2 decimal places, e.g. 52.75) the absolute tolerance is +/-0.02 Find mean and the standard deviation. The mean = 0.248 and SD = 0.067. The mean = 0.428 and SD = 0.076. The mean = 0.248 and SD = 0.076. The mean = 0.284 and SD = 0.076. Which of the following best interprets the standardized statistic in the context of this study? The number of standard deviations the observed proportion is above 0.25 in the null distribution. The number of standard deviations the observed proportion is above 0.42 in the null distribution. The number of standard deviations the observed proportion is below 0.50 in the null distribution. The number of standard deviations the observed proportion is above 0.50 in the null distribution. Based on the standardized statistic, select the best conclusion that you would draw about the research question of whether students tend to have a genuine preference for the number 3 when given the choices 1, 2, 3, and 4. We have very strong evidence that the long-run proportion of people who will pick the number 3 is greater than 25% We have little to no evidence that the long-run proportion of people who will pick the number 3 is greater than 25% We have strong evidence that the long-run proportion of people who will pick the number 3 is greater than 25% We have moderate evidence that the long-run proportion of people who will pick the number 3 is greater than 25% Chapter 01.4 Exercise Question 08 1.4.8 Divine providence? Use the following information to answer the next four questions. Dr. John Arbuthnot (1667-1735) was physician to England's Queen Anne. He was also one of the first scientists to publish a use of p-values and to apply the logic of statistical inference. His goal was to prove the existence of God, and he took as evidence the fact that for 82 years in a row male christenings had outnumbered female christenings. His argument: The p-value is so extremely tiny that the extra male births cannot be due to chance. Therefore the excess males must be due to \"Divine Providence.\" Here is a summary of his data: What was Dr. Arbuthnot's research hypothesis? The long-run proportion of female births is less than 50%. The long-run proportion of male births is less than 50%. The long-run proportion of female births is greater than 50%. The long-run proportion of male births is greater than 50%. LINK TO TEXT Let be Arbuthnot's parameter. Tell in words what refers to. the long-run proportion of male births the long-run proportion of female births the short-run proportion of male births the short-run proportion of female births LINK TO TEXT Explain Dr. Arbuthnot's null hypothesis in words and then in symbols. Null: The short-run proportion of male births is 50%. Null: =0.50. Null: The long-run proportion of female births is 50%. Null: =0.50. Null: The short-run proportion of female births is 50%. Null: =0.50. Null: The long-run proportion of male births is 50%. Null: =0.50. LINK TO TEXT Was Arbuthnot's alternative hypothesis one-sided or two-sided? Give your reasoning. Alt: one-sided. He wanted to demonstrate that male births outnumbered female births. Alt: one-sided. He wanted to demonstrate that female births outnumbered male births. Alt: two-sided. He wanted to demonstrate that male births outnumbered female births. Alt: two-sided. He wanted to demonstrate that female births outnumbered male births. LINK TO TEXT Chapter 01.4 Exercise Question 24 1.4.24 Can domestic dogs understand human body cues such as bowing, pointing, or glancing? The experimenter presented a body cue toward one of two objects and recorded whether or not the dog being tested correctly chose the object indicated. A four-year-old male pit bull named Krieger participated in this study. He chose the correct object 6 out of 10 times when the experimenter turned and looked towards the correct object. Instead of looking at the object, the experimenter kept her eyes on the dog and leaned toward the object. For this part of the study, Krieger got 9 right out of 10. Use the One Proportion applet to develop a null distribution for this scenario. Based on the study's result and your null distribution, calculate a standardized statistic. (Round answer to 1 decimal place, e.g. 5.2) the absolute tolerance is +/-0.2 LINK TO TEXT Strength of evidence: The p-value for this test is 0.01. What are your conclusions based on this p-value? Are the conclusions the same if you base them off the standardized-statistic found above in part (a)? Using both the p-value and the standardized statistic, we have weak evidence that the long-run proportion of times that Krieger makes the correct choice is more than 50%. Using both the p-value and the standardized statistic, we have strong evidence that the long-run proportion of times that Krieger makes the wrong choice is more than 60%. Using both the p-value and the standardized statistic, we have strong evidence that the long-run proportion of times that Krieger makes the correct choice is more than 50%. Using both the p-value and the standardized statistic, we have strong evidence that the long-run proportion of times that Krieger makes the correct choice is less than 30%. LINK TO TEXT Chapter 01.5 Exercise Question 09 1.5.9 According to statistician Persi Diaconis, the probability of a penny landing heads when it is spun on its edge is only about 0.20. Suppose you doubt this claim and think that it should be more than 0.20. To test this, you spin a penny 12 times and it lands heads side up 5 times. You put this information in the One Proportion applet and determine a simulation-based p-value of 0.0770, but the one-proportion z-test pvalue is 0.0303. Which of the following are correct hypotheses for this study? Null: The long-run proportion of times that a penny lands heads when spun is 0.0770 Alt: The long-run proportion of times that a penny lands heads when spun is < 0.0770 Null: The long-run proportion of times that a penny lands tails when spun is 0.2 Alt: The long-run proportion of times that a penny lands tails when spun is > 0.2 Null: The long-run proportion of times that a penny lands heads when spun is 0.2 Alt: The long-run proportion of times that a penny lands heads when spun is > 0.2 Null: The long-run proportion of times that a penny lands heads when spun is 2.0 Alt: The long-run proportion of times that a penny lands heads when spun is > 2.0 LINK TO TEXT Which p-value is the most valid? Why? The simulation based p-value of 0.0303, because the validity conditions are met. There are at least 10 times where the penny landed heads and at least 10 times where the penny landed tails in the sample. The simulation based p-value of 0.077, because the validity conditions are not met. There are not at least 10 times where the penny landed heads and at least 10 times where the penny landed tails in the sample. The one-proportion z-test p-value of 0.077, because the validity conditions are met. There are not at least 10 times where the penny landed heads and at least 10 times where the penny landed tails in the sample. The one-proportion z-test p-value of 0.0303, because the validity conditions are met. There are 10 times where the penny landed heads and 10 times where the penny landed tails in the sample. LINK TO TEXT Do you have strong evidence that a spun penny will land heads more that 20% of the time in the long run? Yes, we do have strong evidence that a penny will land heads more than 20% of the time in the long run, since the p-value is 0.077. No, we do not have strong evidence that a penny will land heads more than 20% of the time in the long run, since the p-value is only 0.077. No, we do not have strong evidence that a penny will land heads more than 20% of the time in the long run, since the p-value is only 0.0303. Yes, we do have strong evidence that a penny will land heads more than 20% of the time in the long run, since the p-value is 0.0303. LINK TO TEXT Chapter 01.5 Exercise Question 15 1.5.15 A recent study (Ackerman, Griskevicius, and Li, 2011) examined expressions of commitment between two partners in a committed romantic relationship. One aspect of the study involved 47 heterosexual couples who are part of an online pool of people willing to participate in surveys. These 47 couples were asked about which person was the first to say \"I love you.\" For 7 of those couples, the two people disagreed about the answer to this question. But both people agreed for the other 40 couples, so those 40 responses were included in the analysis. Previous studies have suggested that males tend to say \"I love you\" first. They found that the man said \"I love you\" in 28 of the 40 couples before the woman did. Since previous research indicated that the man tends to say \"I love you\" before the woman, we tested to see if the probability a man would say \"I love you\" before the woman is more than 50%. Which of the following states the appropriate null and alternative hypotheses for testing whether males are more likely to say "I love you" first? Null: The long-run proportion of times that the female says \"I love you\" first is 50%. Alt: The long-run proportion of times that the female says \"I love you\" first is more than 50%. Null: The long-run proportion of times that the male says \"I love you\" first is less than 50%. Alt: The long-run proportion of times that the male says \"I love you\" first is less than 50%. Null: The long-run proportion of times that the male says \"I love you\" last is 50%. Alt: The long-run proportion of times that the male says \"I love you\" last is more than 50%. Null: The long-run proportion of times that the male says \"I love you\" first is 50%. Alt: The long-run proportion of times that the male says \"I love you\" first is more than 50%. LINK TO TEXT Using an appropriate applet, find the p-value using a theory-based test (one-proportion z-test; normal approximation). (Round your answer to 4 decimal places; e.g. 5.2751.) the absolute tolerance is +/-0.0001 LINK TO TEXT Summarize the conclusion from the p-value. We have strong evidence that the long-run proportion of times that the male says \"I love you\" first is more than 50% We have moderate evidence that the long-run proportion of times that the male says \"I love you\" first is more than 50% We have very strong evidence that the long-run proportion of times that the male says \"I love you\" first is more than 50% We have no evidence that the long-run proportion of times that the male says \"I love you\" first is more than 50% LINK TO TEXT Interpret the meaning of the standardized statistic. The observed proportion of males that say "I love you" first is 2.53 standard deviations away from the null hypothesized value of 0.50 The observed proportion of males that say "I love you" first is 2.53 standard deviations below the null hypothesized value of 0.50 The observed proportion of males that say "I love you" first is 2.53 standard deviations above the null hypothesized value of 0.50 LINK TO TEXT Without using an applet, determine the value of the theory-based (normal approximation) p-value if we used a two-sided alternative hypothesis. (Round your answer to 4 decimal places; e.g. 5.2751.) the absolute tolerance is +/-0.0001 LINK TO TEXT Chapter 02.1 Exercise Question 12 2.1.12 In order to estimate the typical amount of TV watched per day by students at her school of 1,000 students, a student has all of the students in her statistics class (30 students) take a short survey, finding that, on average, students in her statistics class report watching 1.2 hours of television per day. Identify the variable measured on each student. LINK TO TEXT Is the variable categorical or quantitative? LINK TO TEXT Identify two statistics that the student could use to summarize the variable. Mean or Mode. Median or Mode. Mean or Median. Mean or Proportions LINK TO TEXT Identify one graph that the student could use to summarize the variable. Scatter Plot Pie chart Dotplo t Line graph Bar graph LINK TO TEXT Chapter 02.1 Exercise Question 22 2.1.22 In order to estimate the proportion of all likely voters who will likely vote for the incumbent in the upcoming city's mayoral race, a random sample of 267 likely voters is taken, finding that 65% state they will likely vote for the incumbent. The polling agency wishes to test whether there is evidence that more than 50% of likely voters will likely vote for the incumbent. Evaluate the strength of evidence for this hypothesis. Find the p-value for the hypothesis using a simulation-based approach. Based on the p-value evaluate the strength of evidence and state a conclusion about the likely voting outcome in the mayoral race if the election were to take place today. There is strong evidence that a majority of city voters will vote for the incumbent. There is weak evidence that a majority of city voters will vote for the incumbent. There is no evidence that a majority of city voters will vote for the incumbent. LINK TO TEXT To which population, if any, are you comfortable drawing your conclusion? Why? The result generalizes to all U.S. citizens since it came from a random sample. The result does not generalize beyond the sample, since it was not a random sample. The result generalizes to all city voters since it came from a random sample. LINK TO TEXT If a theory-based approach would be reasonable for these data, find the p-value and comment on the similarity of the p-value from the theory-based approach to the p-value you found in (a). If a theory-based approach would not be reasonable for these data, explain why not. Using theory-based methods is appropriate, and the obtained p-value is close to 1. Using theory-based methods is not appropriate, as the obtained p-value is different. Using theory-based methods is not appropriate, as the sample size is too small. Using theory-based methods is appropriate, and the obtained p-value is 0. LINK TO TEXT Chapter 02.2 Exercise Question 07 2.2.7 An instructor collected data on the number of U.S. states her students had visited. A dotplot for the collected data is shown below. Identify the observational units. LINK TO TEXT An instructor collected data on the number of U.S. states her students had visited. Identify the variable recorded and whether it is categorical or quantitative. LINK TO TEXT An instructor collected data on the number of U.S. states her students had visited. A dotplot for the collected data is shown below. Describe what the graph tells us about distribution of the variable recorded. Be sure to comment on shape, center, and variability. LINK TO TEXT An instructor collected data on the number of U.S. states her students had visited. Her class has 50 students. A dotplot for the collected data is shown below. Use the dotplot to find and report the median value for the number of states visited by the students in this study. 7 7.5 8.5 8 LINK TO TEXT An instructor collected data on the number of U.S. states her students had visited. A dotplot for the collected data is shown below. Would the mean value for these data be smaller than, larger than, or the same as the median, as reported in (d)? LINK TO TEXT Suppose that the observation recorded as 43 states is a typo and was meant to be 34. If we corrected this entry in the data set, how would the following numerical statistics change, if at all? Mean: Median: Standard deviation: LINK TO TEXT Chapter 02.2 Exercise Question 19 2.2.19 Needles! Consider a manufacturing process that is producing hypodermic needles that will be used for blood donations. These needles need to have a diameter of 1.65 mmtoo big and they would hurt the donor (even more than usual), too small and they would rupture the red blood cells, rendering the donated blood useless. Thus, the manufacturing process would have to be closely monitored to detect any significant departures from the desired diameter. During every shift, quality control personnel take a random sample of several needles and measure their diameters. If they discover a problem, they will stop the manufacturing process until it is corrected. For now, suppose that a \"problem\" is when the sample average diameter turns out to be statistically significantly different from the target of 1.65 mm. Identify the variable of interest and whether the variable is categorical or quantitative. LINK TO TEXT Write the appropriate hypotheses using appropriate symbols to test whether the average diameter of needles from the manufacturing process is different from the desired value. LINK TO TEXT Suppose that the most recent random sample of 35 needles have an average diameter of 1.64 mm and a standard deviation of 0.07 mm. Assign appropriate symbols to these numbers. LINK TO TEXT Chapter 02.3 Exercise Question 04 2.3.4 Suppose that you perform a significance test and, based on the p-value, decide to reject the null hypothesis at the = 0.05 significance level. Then suppose that your colleague decides to conduct the same test on the same data but using = 0.10 as significance level. For the new significant level, would you reject the null hypothesis, fail to reject the null hypothesis, or would you not have enough information to say? (Hint: First ask yourself what must be true about the p-value based on your decision to reject the null hypothesis at the = 0.05 significance level.) LINK TO TEXT Suppose that you perform a significance test and, based on the p-value, decide to reject the null hypothesis at the = 0.05 significance level. Then suppose that your colleague decides to conduct the same test on the same data but using = 0.01 as significance level. For the new significant level, would you reject the null hypothesis, fail to reject the null hypothesis, or would you not have enough information to say? (Hint: First ask yourself what must be true about the p-value based on your decision to reject the null hypothesis at the = 0.05 significance level.) LINK TO TEXT Suppose that you perform a significance test and, based on the p-value, decide to reject the null hypothesis at the = 0.05 significance level. Then suppose that your colleague decides to conduct the same test on the same data but using = 0.0001 as significance level. For the new significant level, would you reject the null hypothesis, fail to reject the null hypothesis, or would you not have enough information to say? (Hint: First ask yourself what must be true about the p-value based on your decision to reject the null hypothesis at the = 0.05 significance level.) LINK TO TEXT Suppose that you perform a significance test and, based on the p-value, decide to reject the null hypothesis at the = 0.05 significance level. Then suppose that your colleague decides to conduct the same test on the same data but using = 0.065 as significance level. For the new significant level, would you reject the null hypothesis, fail to reject the null hypothesis, or would you not have enough information to say? (Hint: First ask yourself what must be true about the p-value based on your decision to reject the null hypothesis at the = 0.05 significance level.) LINK TO TEXT Chapter 02.3 Exercise Question 24 2.3.24 Do voters make judgments about a political candidate based on his/her facial appearance? Can you correctly predict the outcome of an election, more often than not, simply by choosing the candidate whose face is judged to be more competent-looking? Researchers investigated this question in a study published in Science (Todorov, Mandisodka, Goren, and Hall, 2005). Participants were shown pictures of two candidates and asked who has the more competent-looking face. Researchers then predicted the winner to be the candidate whose face was judged to look more competent by most of the participants. In particular, the researchers predicted the outcomes of the 32 U.S. Senate races in 2004. Because we are looking for evidence that this method works better than guessing we will state: Null hypothesis: The probability this method predicts the winner between the two candidates equals 0.50 ( = 0.50). Alternative hypothesis: The probability this method predicts the winner is greater than 0.50 ( > 0.50). The researchers found the competent-face method of predicting election outcomes to be successful in 23 of the 32 Senate races. Describe what Type I error means in this context. LINK TO TEXT Describe what Type II error means in this context. Deciding the LINK TO TEXT Determine the p-value using the one-proportion applet. Based on this p-value, would you reject the null hypothesis at the 0.01 significance level? LINK TO TEXT Based on your answer to part (c), you could possibly be making Type I error? No Yes LINK TO TEXT "iII-ii'--iii-Singtel 36 3:54 PM CE} 77%l:l'f < The dataset for the last question 0... a The dataset for the last question of quiz one 7 Aug 2017, 7131 AM Dear all, Pls see the dataset of the last question of quiz one below: To investigate this, a professor collected data in her class. Here is the table of responses from her students: Ii-_ll-_ ail J 3 5 Courses Calendar To do Notifications Messages