s2 u3 stats
A therapist wanted to determine if yoga or meditation is better for relieving stress. The therapist recruited 100 of her high-stress patients. Fifty of them were randomly assigned to take weekly yoga classes, and the other 50 were assigned weekly meditation classes. After one month, 30 of the 50 patients in the yoga group reported less stress, and 35 of the 50 patients in the meditation group reported less stress. Assuming the conditions for inference are met, what is the 95% confidence interval for the difference in proportions of patients experiencing stress relief from the yoga and meditation groups? Find the z-table here.
D. (0.60-0.70)+- 1.96
In a small town of 5,832 people, the mayor wants to determine if there is a difference in the proportion of voters ages 18-30 who would support an increase in the food tax, and the proportion of voters ages 31-40 who would support an increase in the food tax. An assistant to the mayor surveys 85 randomly chosen voters ages 18-30, and finds that 62 support the increase. A random sample of 70 voters ages 31-40 is also surveyed, and 56 support the increase. Assuming the conditions for inference have been met, what is the 99% confidence interval for the difference in proportions of voters who would support the increase in the food tax for the different age groups? Find the z-table here.
D. (0.73-0.80) +- 2.58
A statistics student wants to survey a high school of 910 students concerning support for increasing the number of student parking spots. The student randomly selects 90 students, and finds that 63 support increasing the number of student parking spots. Assuming the conditions for inference have been met, what is the 95% confidence interval for the true proportion of students who would support the increase in the number of parking spots?
D. (point estimate) 0.70 +-1.96
What is the z* critical value for constructing a 99% confidence interval for a proportion? Find the z-table here.
D. 2.58
The maker of a cell phone screen protector would like to estimate the proportion of customers who file a warranty claim. To do so, they select a random sample of 200 customers and determine that the 96% confidence interval for the true proportion of customers who file a warranty claim to be 0.15 to 0.28. Which of these statements is a correct interpretation of the confidence level?
D. If many random samples of size 200 are selected from the population of all customers, about 96% of the intervals constructed from the samples would capture the true proportion of customers who file a warranty claim.
Heather runs a successful lawn-mowing business. She would like to estimate the true mean amount of time it takes for her employees to mow a lawn. To do so, she selects a random sample of 30 customers and records the time it takes the employees to mow their lawns. The 90% confidence interval for the true mean time it takes her employees to mow a lawn is 40 to 55 minutes. Which of these statements is a correct interpretation of the confidence level?
D. If many random samples of size 30 are selected from the population of all customers, approximately 90% of the constructed intervals would capture the true mean time it takes for her employees to mow a lawn.
A school nurse would like to estimate the true mean amount of sleep that students at the high school get per night. To do so, she selects a random sample of 30 students and determines that the 90% confidence interval for the true mean number of hours of sleep that high school students get per night to be 6.5 to 7.5 hours. Which of these statements is a correct interpretation of the confidence level?
D. If many random samples of size 30 are selected from the population of all students, about 90% of the intervals would capture the true mean number of hours of sleep that students of this high school get per night.
Sam runs a large chain of car repair shops. He pays his employees for 8 hours of work each day. The employees have to log the amount of time they spend working on each job, which results in a number of billable hours for each employee each day. Sam would like to estimate the mean number of billable hours for the large number of employees at the company. To do so, he selects a random sample of 10 employees and asks them how many billable hours they tend to have each day. From their responses, he constructs a 95% confidence interval for the true mean number of billable hours for all employees in the company. Which of the following may have an impact on the confidence interval, but is not accounted for by the margin of error? response bias nonresponse bias sampling variation undercoverage bias
NOT C
A political candidate feels that she performed particularly well in the most recent debate against her opponent. Her campaign manager polled a random sample of 400 likely voters before the debate and a random sample of 500 likely voters after the debate. The 95% confidence interval for the true difference (post-debate minus pre-debate) in proportions of likely voters who would vote for this candidate was (-0.014, 0.064). What was the difference (pre-debate minus post-debate) in the sample proportions of likely voters who said they will vote for this candidate?
A. (0.064+(-0.014))/2 = 0.025
A teacher has two large containers filled with blue, red, and green beads. He wants his students to estimate the difference in the proportion of red beads in each container. Each student shakes the first container, randomly selects 50 beads, counts the number of red beads, and returns the beads to the container. The student repeats this process for the second container. One student sampled 13 red beads from the first container and 16 red beads from the second container. Assuming the conditions for inference are met, what is the 95% confidence interval for the difference in proportions of red beads in each container? Find the z-table here.
A. (0.26-0.32) +- 1.96
The owner of a popular coffee shop wants to determine if there is a difference between the proportion of customers who use their own cups when they purchase a coffee beverage, and the proportion of customers who use their own cups when they purchase an espresso beverage. Customers using their own cups get a 5% discount, which is displayed on the receipt. The owner randomly selects 50 receipts from all coffee purchases and 50 receipts from all espresso purchases. For coffee purchases, 24 receipts showed that the customer used their own cup. For espresso purchases, 18 receipts showed that the customer used their own cup. Assuming the conditions for inference have been met, what is the 99% confidence interval for the difference in proportion of customers who use their own cups? Find the z-table here.
A. (0.48-0.36) +- 2.58
A student believes that a certain number cube is unfair and is more likely to land with a six facing up. The student rolls the number cube 45 times and the cube lands with a six facing up 12 times. Assuming the conditions for inference have been met, what is the 99% confidence interval for the true proportion of times the number cube would land with a six facing up?
A. (point estimate) 0.27 +-2.58
After a hailstorm, a large car dealership wants to determine the proportion of cars that have damage. The service department randomly selects 50 cars on the dealership lot, examines them, and determines that 18 have damage. Assuming all conditions have been met, they construct a 99% confidence interval for the true proportion of cars with damage from the storm. What are the calculations for this interval?
A. (point estimate) 0.36 +- 2.58
What is the z* critical value for constructing a 90% confidence interval for a proportion? Find the z-table here.
A. 1.65
A recent study estimated that 68% of US adults enjoy reading a book while relaxing. How many adults are required for a random sample to obtain a margin of error of at most 0.05 with 90% confidence? Find the z-table here.
A. 236
A clinic measured the systolic blood pressure for a random sample of 10 patients. The resulting 95% confidence interval for the mean systolic blood pressure of all the patients at this clinic was (111.3, 129.5). What was the margin of error for this confidence interval?
A. 9.1
A school principal claims the graduation rate at a school is 96%. Molly, a student at this school, takes a random sample of students and finds the 95% confidence interval for the true proportion of students graduating from this school is (0.934, 0.983). Is it reasonable to conclude the principal's claim is incorrect?
A. No, because the interval contains 0.96.
A quality control inspector selects 12 bottles of apple juice at random from a single day's production. The mean amount of apple juice in the bottles is 298.3 milliliters, and the 95% confidence interval for the true mean amount of juice dispensed per bottle is (296.4, 300.2). Does this interval give the quality control inspector reason to believe that the mean amount of juice in today's bottles differs from 300 milliliters, as the juice label promises?
A. No, since the advertised value of 300 ml is in the confidence interval.
A yogurt company claims that it prints a free yogurt coupon under a randomly selected 20% of its lids. A loyal customer purchases 85 yogurt cups, and records whether each was a winner. After consuming all 85 cups, he is disappointed to see that only 12 (14.1%) of his yogurt cups contained coupon codes. He performs a 99% confidence interval for the proportion of yogurt cups containing coupon codes, obtaining (0.044, 0.238). What conclusion can the customer draw about the yogurt company's claim?
A. The company's claim may be justified because 0.2 is in the confidence interval.
A major car dealership has several stores in a big city. The owner wants to determine if there is a difference in the proportions of SUVs that are sold at stores A and B. The owner gathers the sales records for each store from the past year. A random sample of 55 receipts from store A shows that 30 of the sales were for SUVs. Another random sample of 60 receipts from store B shows that 45 of the sales were for SUVs. Based on the 99% confidence interval, (-0.43, -0.02), is there convincing evidence of a difference in the proportions of sales that are SUVs for the two stores?
A. There is convincing evidence because the entire interval is below 0.
A 95% confidence interval for the true proportion of math students who prefer to use a handheld calculator versus computer software for computations is (0.751, 0.863). Is it reasonable to believe more than 75% of math students prefer to use a handheld calculator versus computer software for computations?
A. Yes, because the entire interval is greater than 0.75.
A producer of 10-ounce bags of pretzels claims that less than 7% of the pretzels in each bag are broken. The 95% confidence interval for the true proportion of broken pretzels in the 10-ounce bags produced by this company is (0.036, 0.067). Is it reasonable to conclude that less than 7% of pretzels in each bag are broken?
A. Yes, because the entire interval is less than 0.07.
After a hailstorm, a large car dealership wants to determine the proportion of cars that have damage. The service department randomly selects 50 cars on the dealership lot, examines them, and finds that 11 cars have damage. They want to construct a 99% confidence interval for the true proportion of cars with damage from the storm. Are the conditions for inference met?
A. Yes, the conditions for inference are met.
The owner of a popular coffee shop wants to determine if there is a difference between the proportion of customers who use their own cups when they purchase a coffee beverage, and the proportion of customers who use their own cups when they purchase an espresso beverage. Customers using their own cups get a 5% discount, which is displayed on the receipt. The owner randomly selects 50 receipts from all coffee purchases and 50 receipts from all espresso purchases. For coffee purchases, 24 receipts showed that the customer used their own cup. For espresso purchases, 18 receipts showed the customer used their own cup. The owner wants to construct a 95% confidence interval for the difference in the proportions of customers who use their own cups. Are the conditions for inference met?
A. Yes, the conditions for inference are met.
A laundry detergent company wants to determine if a new formula of detergent, A, cleans better than the original formula, B. Researchers randomly assign 500 pieces of similarly soiled clothes to the two detergents, putting 250 pieces in each group. After washing the clothes, independent reviewers determine the cleanliness of the clothes on a scale of 1-10, with 10 being the cleanest. The researchers calculate the proportion of clothes in each group that receive a rating of 7 or higher. For detergent A, 228 pieces of clothing received a 7 or higher. For detergent B, 210 pieces of clothing received a rating of 7 or higher. Assuming the conditions for inference are met, what is the 90% confidence interval for the difference in proportions of clothes that receive a rating of 7 or higher for the two detergents? Find the z-table here.
B. (0.91-0.84) +- 1.65
Twenty-four pairs of adult brothers and sisters were sampled at random from a population. The difference in heights, recorded in inches (brother's height minus sister's height), was calculated for each pair. The 95% confidence interval for the mean difference in heights for all brother-and-sister pairs in this population was (-0.76, 4.34). What is the margin of error for the confidence interval?
B. (4.34-(-0.76))/2 = 2.55
Katie selects a simple random sample of 25 students at her large school and finds that 5 of them are planning to try out for the soccer team next year. She wants to construct a confidence interval for p = the proportion of all students at her school who plan to try out for the soccer team next year, but she realizes she hasn't met all the conditions for constructing the interval. Which condition for this procedure has she failed to meet?
B. (np >- 10)
A scientist wants to sample fish from a large aquarium to estimate the true proportion of striped fish. How many fish are required for a random sample to obtain a margin of error of at most 0.06 with 95% confidence? Find the z-table here.
B. 267
The manager of a large manufacturing company wants to estimate the proportion of items that have been manufactured with defects. How many items are required for a random sample to obtain a margin of error of at most 0.04 with 90% confidence? Find the z-table here.
B. 423
A city planner would like to estimate the true mean annual income of all households in the city. She selects a random sample of 50 households and determines that the 99% confidence interval for the true mean annual income of all households in the city to be $42,000-$68,000. Which of these statements is a correct interpretation of the confidence level?
B. If many random samples of size 50 are selected from all households in the city, approximately 99% of the intervals would capture the true mean household income.
A farmer of a large apple orchard would like to estimate the true mean number of suitable apples produced per tree. He selects a random sample of 40 trees from his large orchard and determines with 95% confidence that the true mean number of suitable apples produced per tree is between 375 and 520 apples. If the farmer had selected 160 trees from his large apple orchard rather than 40 trees, what effect would this have had on the margin of error?
B. It would have been cut in half.
A statistics student wants to survey a high school of 910 students concerning support for increasing the number of student parking spots. The student randomly selects 100 students to construct a 95% confidence interval for the true proportion of students who support increasing the number of student parking spots, and finds that 77 students are in support. Are the conditions for inference met?
B. No, the 10% condition is not met.
At a local college, an admissions officer wants to survey the incoming class of 500 first-year students concerning their preference of major. The officer randomly selects 100 of them to complete the survey, and finds that 45 are planning to major in liberal arts. The admissions officer uses the data to construct a 95% confidence interval for the proportion of first-year students who are planning on majoring in liberal arts. Are the conditions for inference met?
B. No, the 10% condition is not met.
In a small town of 5,832 people, the mayor wants to determine the proportion of voters who would support an increase to the food tax. An assistant to the mayor decides to survey 1,000 randomly chosen people to construct a 90% confidence interval for the true proportion of people who would support the increase in food tax. Of the sample, 363 people say they would support the increase. Are the conditions for inference met?
B. No, the 10% condition is not met.
The cafeteria manager at a high school that has 910 students and 75 teachers is considering adding a baked potato bar to the lunch menu. The manager randomly surveys 90 students and 25 teachers, and finds that 50 of the 90 students and 13 of the 25 teachers would purchase from the potato bar. The manager constructs a 99% confidence interval for the difference in the proportions of students and teachers who would purchase lunch on the day the potato bar option is available. Are the conditions for inference met?
B. No, the 10% condition is not met.
A political candidate feels that she performed particularly well in the most recent debate against her opponent. Her campaign manager polled a random sample of 400 likely voters before the debate and a random sample of 500 likely voters after the debate. The 95% confidence interval for the true difference (post-debate minus pre-debate) in proportions of likely voters who would vote for this candidate was (-0.014, 0.064). Based on this interval, what conclusion should the candidate make about the proportion of likely voters who would vote for her in the upcoming election?
B. The candidate cannot conclude that the proportion of likely voters who would vote for her has increased.
A statistics class weighed 20 bags of grapes purchased from the store. The bags are advertised to contain 16 ounces, on average. The class calculated the 90% confidence interval for the true mean weight of bags of grapes from this store to be (15.875, 16.595) ounces. Is the store justified in stating that the average weight of the bags of grapes is 16 ounces?
B. The store may be justified in stating that the average weight of the bags is 16 ounces because 16 ounces is in the confidence interval.
According to a recent random survey of 1,963 high school students, 581 report playing a musical instrument. A 90% confidence interval for the population of high school students who play a musical instrument is constructed. Which statement identifies what is being estimated? Find the z-table here.
B. The true proportion of high school students who play a musical instrument is p.
A local school board claims that there is a difference in the proportions of households with school-aged children that would support starting the school year a week earlier, and the proportion of households without school-aged children that would support starting the school year a week earlier. They survey a random sample of 40 households with school-aged children about whether they would support starting the school year a week earlier, and 30 households respond yes. They survey a random sample of 45 households that do not have school-aged children, and 25 respond yes. Based on the 90% confidence interval, (0.03, 0.36), is there convincing evidence of a difference in the true proportions of households, those with school-aged children and those without school-aged children, who would support starting school early?
B. There is convincing evidence because the entire interval is above 0.
In a statistics activity, students are asked to determine if there is a difference in the proportion of times that a spinning penny will land with tails up, and the proportion of times a spinning dime will land tails up. The students are instructed to spin the penny and the dime 30 times and record the number of times they land tails up. For one student, the penny lands tails side up 18 times, and the dime lands tails side up 20 times. Based on the 98% confidence interval, (-0.36, 0.22), is there evidence of a difference in proportions of tails side up for a penny and a dime?
B. There is not convincing evidence because the interval contains 0.
An animal rescue agent wanted to estimate the true proportion of all animals in shelters that are adopted each month. To do so, she selects a random sample of 100 animals that were in shelters last month and determines that the 95% confidence interval for the true proportion of animals adopted each month is between 0.12 and 0.24. Which of the following would decrease the margin of error?
B. increasing the sample size
Heather runs a successful lawn-mowing business. She would like to estimate the true mean amount of time it takes for her employees to mow a lawn. To do so, she selects a random sample of 30 customers and records the time it takes the employees to mow their lawns. The 90% confidence interval for the true mean time it takes for her employees to mow a lawn is 40-55 minutes. Which of the following would decrease the width of the interval?
B. increasing the sample size
The dean of students at a large college is interested in learning about their opinions regarding the percentage of first-year students who should be given parking privileges in the main lot. He sends out an email survey to all students about this issue. A large number of first-year students reply but very few sophomores, juniors, and seniors reply. Based on the responses he receives, he constructs a 90% confidence interval for the true proportion of students who believe first-year students should be given parking privileges in the main lot to be (0.71, 0.79). Which of the following may have an impact on the confidence interval, but is not accounted for by the margin of error?
B. nonresponse bias
A local school board wants to determine the proportion of households in the district that would support a proposal to start the school year a week earlier. They ask a random sample of 100 households whether they would support the proposal, and 62 households stated that they would. Assuming that conditions have been met, what is the 90% confidence interval for the true proportion of households that would support the proposal?
C. (point estimate) 0.62 +- 1.65
Twenty-four pairs of adult brothers and sisters were sampled at random from a population. The difference in heights, recorded in inches (brother's height minus sister's height), was calculated for each pair. The 95% confidence interval for the mean difference in heights for all brother-and-sister pairs in this population was (-0.76, 4.34). What was the sample mean difference from these 24 pairs of siblings?
C. 1.79 inches
A clinic measured the systolic blood pressure for a random sample of 10 patients. The resulting 95% confidence interval for the mean systolic blood pressure of all the patients at this clinic was (111.3, 129.5). What was the mean systolic blood pressure from the sample of 10 patients?
C. 120.4
An animal rescue agent wanted to estimate the true proportion of all animals in shelters that are adopted each month. To do so, she selects a random sample of 100 animals and determines that the 95% confidence interval for the true proportion of animals adopted each month is between 0.12 and 0.24. Which of these statements is a correct interpretation of the confidence level?
C. If many random samples of size 100 are selected from all records of animals in shelters, approximately 95% of the intervals would capture the true proportion that were adopted.
A college professor would like to estimate the proportion of students who pull an "all-nighter," meaning they study all night for an upcoming exam. She selects a random sample of 100 students from her large college and finds that the 99% confidence interval for the true proportion of students who pull an all-nighter is 0.48 to 0.62. Which of these statements is a correct interpretation of the confidence level?
C. If many random samples of size 100 are selected from all students at this college, approximately 99% of the intervals would capture the true proportion who pull an all-nighter.
A college performs a survey of 424 randomly chosen graduates to estimate the proportion of alumni who are working in the field of their college degree. For example, if a student earned a degree in biology, do they work in the field of biology? Of the 424 alumni, 361 reported that they were working in the field of their college degree. A 98% confidence interval for the true proportion of graduates who are working in the field of their degree is (0.811, 0.892). What is the correct interpretation of the confidence interval?
C. It can be stated with 98% confidence that the proportion of all graduates who are working in the field of their degree is captured by the interval from 0.811 to 0.892.
A computer company wants to determine if there is a difference in the proportion of defective computer chips in a day's production from two different production plants, A and B. A quality control specialist takes a sample of 100 chips from the first hour of production from plant A and determines that there are 12 defective chips. The specialist then takes a sample of 100 chips from the last hour of production from plant B and determines that there are 10 defective chips. He wants to construct a 90% confidence interval for the true difference in proportions of defective chips from a day's production between the two plants. Are the conditions for inference met?
C. No, the randomness condition is not met.
A computer company wants to determine the proportion of defective computer chips from a day's production. A quality control specialist takes a sample of 100 chips from the first hour of production and determines that there are 12 defective chips. He wants to construct a 90% confidence interval for the true proportion of defective chips from a day's production. Are the conditions for inference met?
C. No, the randomness condition is not met.
A teacher has a large container of blue, red, and green beads. She wants her students to estimate the proportion of red beads. Each student selects 50 beads, counts the number of red beads, and returns the beads to the container. One student sample has 15 red beads. The students are asked to construct a 95% confidence interval for the true proportion of red beads in the container. Are the conditions for inference met?
C. No, the randomness condition is not met.
An inspector inspects large truckloads of potatoes to determine the proportion with blemishes prior to using the potatoes to make potato chips. She intends to compute a 95% confidence interval for this proportion. To do so, she selects a simple random sample of 90 potatoes, and finds 12 with blemishes. The 95% confidence interval is (0.063, 0.204). What is the correct interpretation for this confidence interval?
C. The inspector can be 95% confident that the interval from 0.063 to 0.204 captures the proportion of all potatoes on the truck with blemishes.
A researcher for a polling organization used a random sample of 1,540 residents in a city to construct a 95 percent confidence interval for the proportion of voters who would vote for candidate Jones. The resulting confidence interval was 0.480 ± 0.025. What is the correct interpretation of the confidence interval?
C. The polling organization can be 95% confident that the interval from 0.455 to 0.505 captures the proportion of all city voters who would vote for Jones.
A researcher takes a random sample of 2,496 drivers and finds that 1,603 put their phone in "drive mode" to not be distracted while driving. A 90% confidence interval for the proportion of drivers who use "drive mode" on their phones is (0.626, 0.658). Which statement correctly interprets the interval?
C. The researcher can be 90% confident that the interval from 0.626 to 0.658 captures the true proportion of all drivers who use "drive mode."
In a small town of 5,832 people, the mayor claims that there is a difference in the proportion of voters ages 18-30 who would support an increase in the food tax and the proportion of voters ages 31-40 who would support an increase in the food tax. An assistant to the mayor surveys 85 randomly chosen voters ages 18-30, and finds that 62 support the increase. A random sample of 70 voters ages 31-40 is also surveyed, and 56 support the increase. Based on the 99% confidence interval, (-0.25, 0.10), is there convincing evidence of a difference in the true proportion of voters ages 18-30 and ages 31-40 who would support an increase to the food tax?
C. There is not convincing evidence because the interval contains 0, indicating there might not be a difference.
A statistics class weighed 20 bags of grapes purchased from the store. The bags are advertised to contain 16 ounces, on average. The class calculated the 90% confidence interval for the true mean weight of bags of grapes from this store to be (15.875, 16.595) ounces. What is the correct interpretation of the 90 percent confidence interval?
C. We are 90% confident that the interval from 15.875 ounces to 16.595 ounces captures the true mean weight of bags of grapes.
Nick selects a simple random sample of 25 seniors at his large school and finds that 20 of them eat a healthy breakfast. He wants to construct a confidence interval for p = the proportion of all seniors at this school who eat a healthy breakfast, but he realizes he hasn't met all the conditions for constructing the interval. Which condition for this procedure has he failed to meet?
C. n(1-p) >- 10
A farmer of a large apple orchard would like to estimate the true mean number of suitable apples produced per tree. He selects a random sample of 40 trees from his large orchard and determines with 95% confidence that the true mean number of suitable apples produced per tree is between 375 and 520 apples. Which of the following can be accounted for by the margin of error of this interval?
C. sampling variation
An animal rescue agent wanted to estimate the true proportion of all animals in shelters that are adopted each month. To do so, she selects a random sample of 100 animals that were in shelters last month and determines that the 95% confidence interval for the true proportion of animals adopted is between 0.12 and 0.24. This interval has a margin of error of 0.06. Which of the following can be accounted for by the margin of error?
C. sampling variation
A college professor would like to estimate the proportion of students who pull an "all-nighter," meaning they study all night for an upcoming exam. She selects a random sample of 100 students from her large college and finds that the 99% confidence interval for the true proportion of students who have pulled an all-nighter to be 0.48 to 0.62. If the professor had randomly selected 50 students rather than 100 students, what effect would this have had on the width of the interval?
D. It would have been larger, but it would not have doubled.
A city planner would like to estimate the true mean annual income of all households in the city. She selects a random sample of 50 households and determines that the 99% confidence interval for the true mean annual income of all households in the city to be $42,000 to $68,000. If the city planner had selected 100 households rather than 50 households, what effect would this have had on the margin of error of the interval?
D. It would have been smaller, but it would not have been cut in half.
Ellen's mom thinks the local weather forecaster correctly predicts the weather 85% of the time, but Ellen thinks it is less than that. The 95% confidence interval for the true proportion of correct forecasts by this weather forecaster is (0.796, 0.862). Is it reasonable to believe the true proportion of times this weather forecaster correctly predicts the weather is less than 85%?
D. No, because there are values in the interval that are greater than 0.85.
A recent report stated that over half of food delivery drivers eat some of the food they are delivering. A 95% confidence interval for the true proportion of food delivery drivers who eat some of the food they are delivering is (0.398, 0.706). Is it reasonable to believe more than half of food delivery drivers eat some of the food they are delivering?
D. No, because there are values less than 0.50 in the interval.
A local school board wants to estimate the difference in the proportion of households with school-aged children that would support starting the school year a week earlier, and the proportion of households without school-aged children that would support starting the school year a week earlier. They survey a random sample of 40 households with school-aged children about whether they would support starting the school year a week earlier, and 38 households respond yes. They survey a random sample of 45 households that do not have school-aged children, and 25 respond yes. The school board plans to construct a 90% confidence interval for the difference in proportions of households who would support starting the school year a week earlier. Are the conditions for inference met?
D. No, the Large Counts Condition is not met.
A guidance counselor is studying test anxiety in freshman students. A random sample of 972 high school freshmen finds that 219 of these students have had some form of test anxiety. A 95% confidence interval for the proportion of freshmen with test anxiety is (0.199, 0.252). Which statement correctly interprets the interval?
D. The guidance counselor can be 95% confident that the interval from 0.199 to 0.252 captures the true proportion of all freshmen who have test anxiety.
A teacher has two large containers filled with blue, red, and green beads, and claims the proportions of red beads are the same in each container. Each student shakes the first container, selects 50 beads, counts the number of red beads, and returns the beads to the container. The student repeats this process for the second container. One student's samples contained 13 red beads from the first container and 16 red beads from the second container. Based on the 95% confidence interval, (-0.24, 0.11), is the teacher's claim justified?
D. The teacher's claim might not be justified because the interval contains both positive and negative values. It is plausible that the proportion of red beads in each container is different.
A newspaper poll found that 54% of the respondents in a random sample of voters in the city plan to vote for candidate Roberts. A 95 percent confidence interval for the population proportion is 0.54 ± 0.06. What is the correct interpretation of the 95% confidence interval?
D. We are 95% confident that the interval from 0.48 to 0.60 captures the true proportion of voters who would vote for Roberts.
A school nurse would like to estimate the true mean amount of sleep that students at the high school get per night. To do so, she selects a random sample of 30 students and determines that the 90% confidence interval for the true mean amount of sleep that high school students get per night to be 6.5 to 7.5 hours. Which of the following would decrease the width of the interval?
D. decreasing the confidence level
