Category 1
In a certain region of the United States, the distribution of the number of siblings an individual has is strongly skewed to the right with a mean of 1.8 siblings. Which of the following is a possible value for the median of this distribution?
A) 1 B) 2 C) 3 D) 4 E) 5
In a certain region of the United States, the distribution of the number of siblings an individual has is strongly skewed to the right with a mean of 1.8 siblings. Which of the following is a possible value for the median of this distribution?
A) 1 B) 2 C) 3 D) 4 E) 5
Professor X has 6 snake plants at her home. Two are small, two are medium, and two are large. She wants to see if the plants will grow taller if they are given water from her fish tank. She puts all the plants in her bay window at home so they receive equal amounts of sunlight. For the two small plants, she flips a coin to determine which one will get the water from the fish tank. She does the same for the medium, and large plants. She waters them this way weekly for 10 weeks. After 10 weeks she compares the difference in growth for each set of 2 plants. Which of the following is the best description of the method she is using for data collection?
A) observational study
B) double-blind observational study
C) experiment with completely randomized design
D) experiment with randomized block design
E) experiment with matched pairs design
Professor Chauvet has 6 snake plants at her home. Two are small, two are medium, and two are large. She wants to see if the plants will grow taller if they are given water from her fish tank. She puts all the plants in her bay window at home so they receive equal amounts of sunlight. For the two small plants, she flips a coin to determine which one will get the water from the fish tank. She does the same for the medium, and large plants. She waters them this way weekly for 10 weeks. After 10 weeks she compares the difference in growth for each set of 2 plants. Which of the following is the best description of the method she is using for data collection?
A) observational study
B) double-blind observational study
C) experiment with completely randomized design
D) experiment with randomized block design
E) experiment with matched pairs design
Which of the following scenarios is an experiment?
A) A teacher plays classical music while his students take a test to determine if it will increase scores compared to last test
B) A state cop uses a radar gun to measure the speed of the next 50 cars passing by
C) A firefighter records how many gallons of water are used to extinguish a fire each time they assist at a building fire
D) A doctor asks his patients if they have nay side effects with a certain medication and records their responses
E) A farmer notices that the crops that are planted on the east side of the property do not grow as well as those that are planted on the west side of the property
Which of the following scenarios is an experiment?
A) A teacher plays classical music while his students take a test to determine if it will increase scores compared to last test
B) A state cop uses a radar gun to measure the speed of the next 50 cars passing by
C) A firefighter records how many gallons of water are used to extinguish a fire each time they assist at a building fire
D) A doctor asks his patients if they have nay side effects with a certain medication and records their responses
E) A farmer notices that the crops that are planted on the east side of the property do not grow as well as those that are planted on the west side of the property
According to a report, more and more young adults are drinking coffee daily. An independent study conducted using a random sample of 500 young adults produces a 95 percent confidence interval for p, the proportion of all young adults who drink coffee daily. The interval was reported to be (0.14, 0.18). Which of the following is correct?
A) The margin of error is 0.04
B) We can conclude the majority of young adults drink coffee daily
C) There's a 95% probability that the true proportion of young adults that drink coffee is between 0.14 and 0.18.
D) We can be 95% confident that the true proportion of young adults that drink coffee daily is between 0.14 and 0.18
E) If this procedure were to be repeated many times, 95% of the resulting confidence intervals will display the true proportion of young adults that drink coffee daily is between 0.14 and 0.18
According to a report, more and more young adults are drinking coffee daily. An independent study conducted using a random sample of 500 young adults produces a 95 percent confidence interval for p, the proportion of all young adults who drink coffee daily. The interval was reported to be (0.14, 0.18). Which of the following is correct?
A) The margin of error is 0.04
B) We can conclude the majority of young adults drink coffee daily
C) There's a 95% probability that the true proportion of young adults that drink coffee is between 0.14 and 0.18.
D) We can be 95% confident that the true proportion of young adults that drink coffee daily is between 0.14 and 0.18
E) If this procedure were to be repeated many times, 95% of the resulting confidence intervals will display the true proportion of young adults that drink coffee daily is between 0.14 and 0.18
Candidate A and Candidate B are running for president. You are planning a survey to determine what proportion of registered voters plan to vote for Candidate A (p). You will contact a random sample of registered voters. You want to estimate p with 99% confidence and a margin of error no greater than 0.01. What is the minimum number of registered voters you will need to survey in order to meet these requirements?
A) 97 B) 166 C) 6,766 D) 9,604 E) 16,590
Candidate A and Candidate B are running for president. You are planning a survey to determine what proportion of registered voters plan to vote for Candidate A (p). You will contact a random sample of registered voters. You want to estimate p with 99% confidence and a margin of error no greater than 0.01. What is the minimum number of registered voters you will need to survey in order to meet these requirements?
A) 97 B) 166 C) 6,766 D) 9,604 E) 16,590
The LSRL equation y-hat = 10 + 2x describes the relationship between x (age in weeks) and y (weight in pounds) for a sample of 50 German Shepherd puppies ages [5, 20] weeks. The weight of a particular German Shepherd puppy that is 10 weeks old is underestimated by 10 pounds. How much does this puppy weigh?
The LSRL equation y-hat = 10 + 2x describes the relationship between x (age in weeks) and y (weight in pounds) for a sample of 50 German Shepherd puppies ages [5, 20] weeks. The weight of a particular German Shepherd puppy that is 10 weeks old is underestimated by 10 pounds. How much does this puppy weigh?
A) 10 pounds B) 20 pounds C) 30 pounds D) 40 pounds E) 50 pounds
The phrase, household penetration, describes the percentage of households that purchase a particular item. The household penetration for toilet paper is 97%. You survey a random sample of 50 households and want to compute the probability that at least one of the households does not purchase toilet paper.
Which of the following is appropriate for modeling this distribution?
A) Binomial B) Geometric C) Normal D) t E) Chi-square
The phrase, household penetration, describes the percentage of households that purchase a particular item. The household penetration for toilet paper is 97%. You survey a random sample of 50 households and want to compute the probability that at least one of the households does not purchase toilet paper.
Which of the following is appropriate for modeling this distribution?
A) Binomial B) Geometric C) Normal D) t E) Chi-square
A game show producer asked 100 randomly selected adults, “Have you ever bungee jumped?” Of the adults surveyed, 14 said “Yes!” Is there convincing statistical evidence that the true proportion of all adults that have bungee jumped is more than 10%?
A) No, because the difference between the sample proportion and population proportion is 0.04, not greater than 0.05
B) No, because the probability of observing a sample proportion at least as large as 0.14, if the population proportion is 0.10, is greater than 0.05
C) Yes, because the probability of observing a sample proportion at least as large as 0.14, if the population proportion is 0.10, is greater than 0.05
D) Yes, because the probability of observing a sample proportion at least as large as 0.14, if the population proportion is 0.10, is less than 0.05
E) Yes, because the difference between the sample proportion and the population proportion is 0.04, which is less than 0.05
A game show producer asked 100 randomly selected adults, “Have you ever bungee jumped?” Of the adults surveyed, 14 said “Yes!” Is there convincing statistical evidence that the true proportion of all adults that have bungee jumped is more than 10%?
A) No, because the difference between the sample proportion and population proportion is 0.04, not greater than 0.05
B) No, because the probability of observing a sample proportion at least as large as 0.14, if the population proportion is 0.10, is greater than 0.05
C) Yes, because the probability of observing a sample proportion at least as large as 0.14, if the population proportion is 0.10, is greater than 0.05
D) Yes, because the probability of observing a sample proportion at least as large as 0.14, if the population proportion is 0.10, is less than 0.05
E) Yes, because the difference between the sample proportion and the population proportion is 0.04, which is less than 0.05
The manager of a landscaping company collected data for an entire summer. Before each job he completely filled the gasoline tank for his mower. After each job, he recorded the square footage of the lawn that was mowed as well as how much gasoline remained in the tank. As expected, larger lawns left him with very little gasoline in the tank. At the end of the season he displayed the data in a scatterplot and saw that the relationship between lawn size and gas remaining was roughly linear. The value of r2 was 0.85. Find and interpret the value of the correlation between the lawn size and the amount of gasoline remaining in the tank at the end of the job.
A) r = 0.72. The linear relationship between lawn size and gas remaining is moderately strong and positive.
B) r = 0.92. The linear relationship between lawn size and gas remaining is strong and positive.
C) r = -0.72. The linear relationship between lawn size and gas remaining is moderately strong and negative.
D) r = -0.92. The linear relationship between lawn size and gas remaining is strong and negative.
E) The value of the correlation cannot be determined without more information.
The manager of a landscaping company collected data for an entire summer. Before each job he completely filled the gasoline tank for his mower. After each job, he recorded the square footage of the lawn that was mowed as well as how much gasoline remained in the tank. As expected, larger lawns left him with very little gasoline in the tank. At the end of the season he displayed the data in a scatterplot and saw that the relationship between lawn size and gas remaining was roughly linear. The value of r2 was 0.85. Find and interpret the value of the correlation between the lawn size and the amount of gasoline remaining in the tank at the end of the job.
A) r = 0.72. The linear relationship between lawn size and gas remaining is moderately strong and positive.
B) r = 0.92. The linear relationship between lawn size and gas remaining is strong and positive.
C) r = -0.72. The linear relationship between lawn size and gas remaining is moderately strong and negative.
D) r = -0.92. The linear relationship between lawn size and gas remaining is strong and negative.
E) The value of the correlation cannot be determined without more information.
An organization that strives to hold agencies accountable for truth in news reporting plans to select a random sample of 100 news stories from major U.S. news agencies in order to estimate the proportion of news stories produced by major U.S. news agencies that contain false information. A 90 percent confidence interval for the proportion of all news stories that contain false information will then be constructed. Before selecting the sample, the organization determines that they want to make the margin of error as small as possible. Which of the following is the best way for them to decrease the margin of error?
A) Increase CL to 95%
B) Increase CL to 99%
C) Include wider diversity of sources, such as local and international agencies
D) Include news stories over a broad period of time, such as the past decade
E) Increase sample size
An organization that strives to hold agencies accountable for truth in news reporting plans to select a random sample of 100 news stories from major U.S. news agencies in order to estimate the proportion of news stories produced by major U.S. news agencies that contain false information. A 90 percent confidence interval for the proportion of all news stories that contain false information will then be constructed. Before selecting the sample, the organization determines that they want to make the margin of error as small as possible. Which of the following is the best way for them to decrease the margin of error?
A) Increase CL to 95%
B) Increase CL to 99%
C) Include wider diversity of sources, such as local and international agencies
D) Include news stories over a broad period of time, such as the past decade
E) Increase sample size
X is an avid tennis player. She kept track of the number of winners she had per game for an entire season. The shape of the distribution of the number of winners is roughly symmetric and the five number summary of the number of winners is:
Min: 10 Q1: 18 Med: 48 Q3: 79 Max: 92
Y is X’s biggest rival. The average number of winners Y had per game for the season has the same value as X’s IQR. Who had the greatest average number of winners this season? Explain.
A) X, she averaged ~48 winners/game, while Y only averaged 18 winners/game.
B) X, she averaged 49.4 winners/game, while Y only averaged 48 winners/game.
C) Y, he averaged 61 winners/game, while X only averaged 48 winners/game.
D) There is not enough info to determine X's average.
X is an avid tennis player. She kept track of the number of winners she had per game for an entire season. The shape of the distribution of the number of winners is roughly symmetric and the five number summary of the number of winners is:
Min: 10 Q1: 18 Med: 48 Q3: 79 Max: 92
Y is X’s biggest rival. The average number of winners Y had per game for the season has the same value as X’s IQR. Who had the greatest average number of winners this season? Explain.
A) X, she averaged ~48 winners/game, while Y only averaged 18 winners/game.
B) X, she averaged 49.4 winners/game, while Y only averaged 48 winners/game.
C) Y, he averaged 61 winners/game, while X only averaged 48 winners/game.
D) There is not enough info to determine X's average.
A dog breeder would like to know how many Dalmatian puppies are typically born in a litter. He conducts some research and selects a random sample of 101 Dalmatian birth records. He examines each birth record and identifies the number of puppies that were born in the litter. The distribution of the number of puppies born per litter was skewed left with a mean of 6.2 puppies born per litter and a standard deviation of 2.1 puppies per litter. He would like to estimate, with 99% confidence, the mean number of puppies born per litter for all Dalmatian births. Which of the following is the correct interval?
A) 6.2 +/- 2.576(0.21)
B) 6.2 +/- 2.576(2.1)
C) 6.2 +/- 2.626(0.21)
D) 6.2 +/- 2.626(2.1)
E) The confidence interval cannot be computed because the distribution of the number of puppies per litter is skewed to the left.
A dog breeder would like to know how many Dalmatian puppies are typically born in a litter. He conducts some research and selects a random sample of 101 Dalmatian birth records. He examines each birth record and identifies the number of puppies that were born in the litter. The distribution of the number of puppies born per litter was skewed left with a mean of 6.2 puppies born per litter and a standard deviation of 2.1 puppies per litter. He would like to estimate, with 99% confidence, the mean number of puppies born per litter for all Dalmatian births. Which of the following is the correct interval?
A) 6.2 +/- 2.576(0.21)
B) 6.2 +/- 2.576(2.1)
C) 6.2 +/- 2.626(0.21)
D) 6.2 +/- 2.626(2.1)
E) The confidence interval cannot be computed because the distribution of the number of puppies per litter is skewed to the left.
Aaron is a good student who enjoys statistics. He sets a goal for himself to do well enough compared to his peers so that his standardized score on his Statistics final is equal to his percentile rank (written as a decimal) among his classmates. Scores on the Statistics final are normally distributed. What goal did he set for himself?
A) 0.25 B) 0.78 C) 0.96 D) 2.25 E) 2.41
Aaron is a good student who enjoys statistics. He sets a goal for himself to do well enough compared to his peers so that his standardized score on his Statistics final is equal to his percentile rank (written as a decimal) among his classmates. Scores on the Statistics final are normally distributed. What goal did he set for himself?
A) 0.25 B) 0.78 C) 0.96 D) 2.25 E) 2.41
A manager of a local fast food restaurant wants to determine the average amount of time it takes from when a customer enters the drive-through line until they receive their order, regardless of the time of the day and the day of the week. That is, he would like to know the true average drive-through wait time for all his customers. Which of the following methods would be most likely to estimate the desired parameter with low bias and low variability?
A) Select a random sample of 100 customers over a period of 1 month, determine each selected customer's wait time, then compute the average wait time for all 100 customers.
B) Select a random sample of 100 customers over a weekend, determine each selected customer's wait time, then compute the average wait time for all 500 customers.
C) Select a random sample of 500 customers on a randomly selected weekday, determine each selected customer's wait time, then compute the average wait time for all 500 customers.
D) Select a random sample of 500 customers over a weekend, determine each selected customer's wait time, then compute the average wait time for all 500 customers.
E) Select a random sample of 500 customers over a period of 1 month, determine each selected customer's wait time, then compute the average wait time for all 500 customers.
A manager of a local fast food restaurant wants to determine the average amount of time it takes from when a customer enters the drive-through line until they receive their order, regardless of the time of the day and the day of the week. That is, he would like to know the true average drive-through wait time for all his customers. Which of the following methods would be most likely to estimate the desired parameter with low bias and low variability?
A) Select a random sample of 100 customers over a period of 1 month, determine each selected customer's wait time, then compute the average wait time for all 100 customers.
B) Select a random sample of 100 customers over a weekend, determine each selected customer's wait time, then compute the average wait time for all 500 customers.
C) Select a random sample of 500 customers on a randomly selected weekday, determine each selected customer's wait time, then compute the average wait time for all 500 customers.
D) Select a random sample of 500 customers over a weekend, determine each selected customer's wait time, then compute the average wait time for all 500 customers.
E) Select a random sample of 500 customers over a period of 1 month, determine each selected customer's wait time, then compute the average wait time for all 500 customers.
Martin desires to grow tall sunflower plants. He wonders how the amount of water he provides the sunflowers will affect their growth. One spring Martin planted 25 sunflower plants, making sure each one had the same soil, amount of space, and exposure to sunlight. The first one received one ounce of water per day. The second one received 2 ounces of water per day, and so on. To determine the ideal amount of water needed, he consistently watered his sunflowers this way and at the end of the summer recorded the height of each sunflower (in cm). Then he performed a regression analysis on the data.
Constant: Coef: 42.5 SE Coef: 8.34 T: 5.1 P: 0.000
Amount of water: Coef: 5.875 SE Coef: 2.191 T: 2.68 P: 0.005
S = 8.0527, R2 = 89.5%, R2(adj) = 87.2%
He conducts a significance test to determine if there's convincing evidence of a positive linear relationship between amount of water his sunflower plants received and how tall they grew. What is the correct test statistic and conclusion? Assume all conditions for inference are met.
A) t=2.68. There is convincing evidence of a positive linear relationship between the amount of water and height of a sunflower.
B) t=2.68. There is not convincing evidence of a positive linear relationship between the amount of water and height of a sunflower.
C) t=5.1. There is convincing evidence of a positive linear relationship between the amount of water and height of a sunflower.
D) t=5.1. There is not convincing evidence of a positive linear relationship between the amount of water and height of a sunflower.
E) t=5.875. There is convincing evidence of a positive linear relationship between the amount of water and height of a sunflower.
Martin desires to grow tall sunflower plants. He wonders how the amount of water he provides the sunflowers will affect their growth. One spring Martin planted 25 sunflower plants, making sure each one had the same soil, amount of space, and exposure to sunlight. The first one received one ounce of water per day. The second one received 2 ounces of water per day, and so on. To determine the ideal amount of water needed, he consistently watered his sunflowers this way and at the end of the summer recorded the height of each sunflower (in cm). Then he performed a regression analysis on the data.
Constant: Coef: 42.5 SE Coef: 8.34 T: 5.1 P: 0.000
Amount of water: Coef: 5.875 SE Coef: 2.191 T: 2.68 P: 0.005
S = 8.0527, R2 = 89.5%, R2(adj) = 87.2%
He conducts a significance test to determine if there's convincing evidence of a positive linear relationship between amount of water his sunflower plants received and how tall they grew. What is the correct test statistic and conclusion? Assume all conditions for inference are met.
A) t=2.68. There is convincing evidence of a positive linear relationship between the amount of water and height of a sunflower.
B) t=2.68. There is not convincing evidence of a positive linear relationship between the amount of water and height of a sunflower.
C) t=5.1. There is convincing evidence of a positive linear relationship between the amount of water and height of a sunflower.
D) t=5.1. There is not convincing evidence of a positive linear relationship between the amount of water and height of a sunflower.
E) t=5.875. There is convincing evidence of a positive linear relationship between the amount of water and height of a sunflower.