Toán SAT MATH Cô Phạm Thảo SURVEYS AND DATA SAMPLES SAMPLES 1 ) Subjects not selected at random Subjects not randomly assigned • Results cannot be generalized to the population • Cause and effect cannot.. Sat SAT math scatterplot
SAT MATH Cô Phạm Thảo SURVEYS AND DATA SAMPLES SAMPLES 1.) Subjects not selected at random & Subjects not randomly assigned • Results cannot be generalized to the population • Cause and effect cannot be proven Example Researchers want to see whether medication X is effective in treating the flu People with the flu from Town A receive medication X People with the flu from Town B receive a placebo (sugar pill) More people in the medication X group experience a reduction in flu symptoms 2.) Subjects not selected at random & Subjects randomly assigned • Results cannot be generalized to the population • Cause and effect can be proven Example Researchers want to see whether medication X is effective in treating the flu People with the flu from Town A and Town B are randomly assigned to either medication X or a placebo (sugar pill) More people in the medication X group experience a reduction in flu symptoms 3.) Subjects selected at random & Subjects not randomly assigned • Results can be generalized to the population • Cause and effect cannot be proven Example Researchers want to see whether medication X is effective in treating the flu People with the flu from the general population are randomly selected They are given the choice of a new medication (medication X ) or a traditional medication (really a sugar pill) More people in the medication X group experience a reduction in flu symptoms 4.) Subjects selected at random & Subjects randomly assigned • Results can be generalized to the population • Cause and effect can be proven Example Researchers want to see whether medication X is effective in treating the flu People with the flu from the general population are randomly selected Using a coin toss (heads or tails), researchers randomly assign each person to either medication X or a placebo (sugar pill) More people in the medication X group experience a reduction in flu symptoms Tích kiến thức, trữ niềm vui SAT MATH Cô Phạm Thảo { RANDOM SAMPLES, BIASED SAMPLES Check whether the data sample represents the larger population If it doesn’t, the survey is biased Question A railroad company is planning to build a new station along one of its busiest lines into the downtown area where many commuters work The of 200 residents who commute to the downtown area for work Over 80 percent of those surveyed are in favor of building the new station Which of the following is true about the survey’s reliability? A It is unreliable because the survey sample is not representative of the entire town B It is unreliable because the survey sample is too small C It is reliable because nobody in the survey sample works for the railroad company D It is reliable because the survey sample excludes people who not ride the train Question A researcher conducted a survey to determine whether people in a certain large town prefer watching robot battles on television or attending robot battes in person The researcher asked 249 people who visited a local coffee shop on a Monday, and people refused to respond Which of the following factors makes it least likely that a reliable conclusion can be drawn about the robot-batte-watching preferences of all people in the town? A The number of people who refused to respond B Where the survey was conducted C Population size D Sample size Question A university wants to determine the dietary preferences of the students in its freshman class Which of the following survey methods is most likely to provide the most valid results? A Selecting a random sample of 600 students from the university B Selecting a random sample of 300 students from the university’s freshman class C Selecting a random sample of 600 students from the university’s freshman class D Selecting a random sample of 600 students from one of the university’s freshman dining halls Question The members of a state senate wanted to assess the opinions of all state residents about renovating the truck stops on the state highways The senate surveyed a sample of 2,800 state residents who drive trucks The survey showed that the majority of those sampled were in favor of the renovations Which of the following is true about the state senate’s survey? A The survey sample should have included more residents who drive trucks B The survey sample should have consisted entirely of residents who not drive trucks C The survey sample is biased because it is not representative of all state residents D It shows the majority of state residents are in favor of the truck stop renovations Question Near the end of a livestreamed makeup tutorial, the influencer invited viewers to respond to a poll on social media that asked," Do you think I should review more lipstick on my channel?" At the end of the livestream, the influencer reported that 34% responded "Yes," and 60% responded "No." Which of the following best explains why the results are unlikely to represent the sentiments of the population of the United States? A The influencer did not allow viewers enough time to respond to the poll Tích kiến thức, trữ niềm vui SAT MATH Cô Phạm Thảo B The percentages not add up to 100%, so any possible conclusions from the poll are invalid C There were not 50% "Yes" responses and 50% "No" responses D Those who responded to the poll were not a random sample of the population of the United States { ASSOCIATION, CAUSATION Question To determine whether low lighting affects reading speed, a researcher randomly selected 30 subjects to participate in a study Half of the subjects were randomly assigned to read an article under low lighting (400 lumens) while the other half read the same article under normal lighting (900 lumens) The resulting data showed that the subjects who read the article under low lighting took significantly longer than those who read the article under normal lighting Based on the design and results of the study, which of the following is an appropriate conclusion? A Low lighting is harmful to the eyes B Everyone reads slower under low lighting C Low lighting is likely to cause a decrease in reading speed D High lighting (1, 200 lumens) is likely to cause an increase in reading speed Question Researchers conducted an experiment to determine whether exercise improves student exam scores They randomly selected 200 students who exercise at least once a week and 200 students who not exercise at least once a week After tracking the students’ academic performances for a year, the researchers found that the students who exercise at least once a week performed significantly better on the same exams than the students who not Based on the design and results of the study, which of the following is an appropriate conclusion? A Exercising at least once a week is likely to improve exam scores B Exercising three times a week improves exam scores more than exercising just once a week C Any student who starts exercising at least once a week will improve his or her exam scores D There is a positive association between exercise and student exam scores Question To determine if smelling lavender oil reduces stress for men, researchers interviewed a random sample of 4,800 men who had no history of stress Study participants were identified as either regular or occasional lavender oil sniffers Ten years later, researchers interviewed the men again They found that the proportion of men who experienced frequent stress was significantly lower for men identified as regular lavender oil sniffers Which of the following is the most appropriate conclusion of the study? A Lavender oil causes a reduction in stress for men but not necessarily for women B Lavender oil causes a reduction in stress for men and women C There is an association between lavender oil use and stress for men, but it is not necessarily a causeand-effect relationship, and the association may not exist for women D There is an association between lavender oil use and stress for men and women, but it is not necessarily a cause-and effect relationship Question In order to determine if treatment A is successful in improving hearing, a research study was conducted From a large population of people with poor hearing, 500 participants were selected at Tích kiến thức, trữ niềm vui SAT MATH Cô Phạm Thảo random Half of the participants were randomly assigned to receive treatment A, and the other half did not receive treatment A The resulting data showed that participants who received treatment A had significantly improved hearing as compared to those who did not receive treatment A Based on the design and results of the study, which of the following is an appropriate conclusion? A Treatment A is likely to improve the hearing of people who have poor hearing B Treatment A improves hearing better than all other available treatments C Treatment A will improve the hearing of anyone who takes it D Treatment A will cause a substantial improvement in hearing Question 10 Researchers must conduct an experiment to see whether a new vaccine is effective in relieving certain allergies They have selected a random sample of 100 allergy patients Some of the patients are assigned to the new vaccine while the rest are assigned to the traditional treatment Which of the following methods of assigning each patient’s treatment is most likely to lead to a reliable conclusion about the effectiveness of the new vaccine? A Females are assigned to the new vaccine B Those who have more than one allergy are assigned to the new vaccine C The patients divide themselves evenly into two groups A coin is tossed to decide which group receives the new vaccine D Each patient is assigned a random number Those with an even number are assigned to the new vaccine { INTERPRETING RESULTS Question 11 A survey was conducted using a sample of bowlers selected at random from the Greater Utah Bowling League The bowlers surveyed were asked to name the manufacturer of their current bowling balls What is the largest population to which the results of the survey can be generalized? A All athletes in the United States B All bowlers in the United States C All bowlers in the Greater Utah Bowling League D All bowlers in Utah Question 12 An economist conducted research to determine whether there is a relationship between the price of food and population density He collected data from a random sample of 100 U.S cities and found significant evidence that the price of food is lower in places with a high population density Which of the following conclusions is best supported by these results? A In U.S cities, there is a positive association between the price of food and population density B In U.S cities, there is a negative association between the price of food and population density C In U.S cities, a decrease in the price of food is caused by an increase in the population density D In U.S cities, an increase in the population density is caused by a decrease in the price of food Question 13 A bottled water company conducts a survey to find out how many bottles of water people consume per day If a representative and random sample data relates to the estimated mean of the entire population? Tích kiến thức, trữ niềm vui SAT MATH A B C D Cô Phạm Thảo The mean of the sample data is equal to the estimated mean of the population The mean of the sample data cannot be used to estimate the mean of the mopulation The mean of the sample data should be multiplied by 100 to get the estimated mean of the population The mean of the sample data should be multiplied by 1,000 to get the estimated mean of the population Question 14 Two candidates are running for governor of a state A recent poll reports that out of a random sample of 250 voters, 110 support Candidate A and 140 support Candidate B An estimated 500,000 state residents are expected to vote on election day According to the poll, Candidate B is expected to receive how many more votes than Candidate A? A 60,000 B 130,000 C 220,000 D 280,000 Question 15 A record of driving violations by type and vehicle is shown below Truck Car Total Speeding 68 83 151 Violation Type Stop Sign Parking 39 17 51 26 90 43 Total 124 160 284 If the data is used to estimate driving violation information about 2,000 total violations in a certain state, which of the following is the best estimate of the number of speeding violations committed by cars in the state? A 479 B 585 C 1063 D 1099 Question 16 A candy company sells jelly beans in five colors: black, green, orange, red, and yellow The company sells boxes of jelly beans, each of which contains 20 individual bags Each individual bag contains 75 jelly beans A customer purchased boxes of jelly beans and selected one bag at random from each box The customer counted the number of each color in each bag The results are shown in the chart below Color Black Green Orange Red Yellow Bag 10 13 22 20 10 Bag 12 11 20 21 11 Bag 13 21 23 10 Bag 11 12 21 21 10 Bag 12 21 22 11 Which of the following is the closest approximation of the total number of green jelly beans in the customer’s purchase? A 60 B 240 C 1,200 D 4,500 Question 17 A department store manager wants to determine why customers return the products they buy The manager surveyed randomly selected dinnerware, of whom 80 percent indicated that at least one piece of dinnerware was chipped or broken Which of the following conclusions is best supported by the sample data? A Most of the products returned to the store contain chipped or broken pieces Tích kiến thức, trữ niềm vui SAT MATH Cô Phạm Thảo B Dinnerware products are more likely to contain chipped or broken pieces than other products C Most customers returning dinnerware returned products containing chipped or broken pieces D At least 80 percent of the products sold at the store contain chipped or broken pieces Question 18 An ecologist selected a random sample of 50 beavers from a river and found that the mean weight of the beavers in the sample was 42 pounds (lbs), with an associated margin of error of 3.1 lbs Which of the following is the best interpretation of the ecologist’s findings? A All beavers in the sample have a weight between 38.9lbs and 45.1lbs B Most beavers in the river have a weight between 38.9lbs and 45.1lbs C Any weight between 38.9lbs and 45.1lbs is a plausible value for the mean weight of the beavers in the sample D Any weight between 38.9lbs and 45.1lbs is a plausible value for the mean weight of beavers in the river Question 19 A researcher surveyed a random sample of retirees from a large retirement home about how often they see their grandchildren Using the sample data, the researcher estimated that 14% of the retirees in the population saw their grandchildren at least once per year The margin of error for this estimation is 3% Which of the following is the most appropriate conclusion about all retirees at the retirement home, based on the given estimate and margin of error? A At least 14% but no more than 17% of the retirees see their grandchildren al least once per year B The researcher is between 11% and 17% sure that most retirees see their grandchildren at least once per year C It is unlikely that less than 14% of the retirees see their grandchildren at least once per year D It is plausible that the percentage of retirees who see their grandchildren at least once per year is between 11% and 17% Question 20 A store manager asked a random sample of shoppers how long they shopped Based on the responses, the estimated mean was found to be 12.5 minutes, with an associated margin of error of 2.5 minutes Which of the following is the best conclusion from these data? A It is likely that all shoppers shopped for between 10 and 15 minutes B It is likely that most shoppers shopped for 12.5 minutes C It is plausible that the mean time spent shopping by all shoppers is between 10 and 15 minutes D It is not possible that any shopper shopped for less than 10 minutes Question 21 Students in a school were surveyed to determine whether they are satisfied with the mattresses in the dorms A random sample of 100 students was selected All 100 responded, and 61% said they are satisfied Based on this information, which of the following statements must be true? I Of all the school’s students, 61% would say they are satisfied with the mattresses in the dorms II If another random sample of 100 students were surveyed, 61% would say they are satisfied A Neither B I only C II only D I and II Question 22 A pollster recently surveyed 3,000 people who were selected at random from a large country and asked each of the adults, "Are you satisfied with the quality of health care in the country? Of those surveyed, 56 percent responded that they were satisfied with the quality of health care in the country Based on the results of the survey, which of the following statements must be true? Tích kiến thức, trữ niềm vui SAT MATH Cô Phạm Thảo I Of all adults in the country, 56 percent are satisfied with the quality of health care in the country II If 3,000 adults selected at random from a different country were surveyed, 56 percent of them would report they are satisfied with the quality of health care in the country III If another 3,000 adults selected at random from the country were surveyed, 56 percent of them would report they are satisfied with the quality of health care in the country A None B II only C I and II only D I and III only Question 23 A market researcher selected 400 people at random from a group of people who indicated that they liked a certain social media influencer The 400 were given a book written by the influencer and then asked whether they liked or disliked the book Of those surveyed, 75% said they liked the book Which of the following inferences can appropriately be drawn from this survey result? A At least 75% of readers will like this book B At least 75% of people who use social media will like this book C Most people who like this influencer will like this book D Most people who use social media will like this book Question 24 A study was conducted on the heights of fourth graders in a particular county A random sample of girls was taken with each girl’s height measured and recorded The sample contained 250 girls, and 20% of the girls were more than 57 inches tall Which of the following conclusions is best supported by the sample data? A Approximately 20% of all fourth-grade girls in the county were taller than 57 inches B Approximately 20% of all fourth-graders in the county were taller than 57 inches C The average height of all fourth-graders in the county was 57 inches D The majority of all fourth-graders in the county are shorter than 57 inches Question 25 The length of a blue-spotted salamander’s tail can be used to estimate its age A biologist selects 80 blue-spotted salamanders at random and finds that the average length of their tails has a 95% confidence interval of to inches Which of the following conclusions is the most appropriate based on the confidence interval? A 95% of all blue-spotted salamanders have a tail that is between and inches in length B 95% of all salamanders have a tail that is between and inches in length C The true average length of the tails of all blue-spotted salamanders is likely between and inches D The true average length of the tails of all salamanders is likely between and inches Question 26 A basketball manufacturer selects a random sample of its basketballs each week to ensure a consistent air pressure within them is maintained In Week , the sample had a mean air pressure of 8.2 psi (pounds per square inch) and a margin of error of 0.1 psi In Week 2, the sample had a mean air pressure of 7.7 psi and a margin of error of 0.3 psi Based on these results, which of the following is a reasonable conclusion? A Most of the basketballs produced in Week had an air pressure under 8.2 psi, whereas most of the basketballs produced in Week had an air pressure under 7.7 psi B The mean air pressure of all the basketballs produced in Week was 0.5 psi more than the mean air pressure of all the basketballs produced in Week C The number of basketballs in the Week sample was more than the number of basketballs in the Week sample Tích kiến thức, trữ niềm vui SAT MATH Cô Phạm Thảo D It is very likely that the mean air pressure of all the basketballs produced in Week was less than the mean air pressure of all the basketballs produced in Week Question 27 For a contest to choose a new soda flavor, consumers could use either social media or a text message to vote for their favorite of two flavors The flavor receiving more than 50% of the vote won As estimated 5% of consumers voted and 80% of the votes were cast on social media Flavor earned 60% of the vores cast on social media and 5% of the votes cast using a text message Based on this information, which of the following is an accurate conclusion? A If all consumers had voted, Flavor would have won B Consumers voting by social media were likely younger than consumers voting by text message C Consumers voting by social media were more likely to prefer Flavor than were consumers voting by text message D If all consumers who voted had voted by social media instead of by text message Flavor would have won Tích kiến thức, trữ niềm vui SAT MATH Cơ Phạm Thảo KEYS Tích kiến thức, trữ niềm vui ... in the sample have a weight between 38.9lbs and 45.1lbs B Most beavers in the river have a weight between 38.9lbs and 45.1lbs C Any weight between 38.9lbs and 45.1lbs is a plausible value for the... the confidence interval? A 95 % of all blue-spotted salamanders have a tail that is between and inches in length B 95 % of all salamanders have a tail that is between and inches in length C The... population Question 14 Two candidates are running for governor of a state A recent poll reports that out of a random sample of 250 voters, 110 support Candidate A and 140 support Candidate B An estimated