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Kevin would like to find out what type of car is the most popular among residents in his neighborhood. There are 25 streets in his neighborhood and each street has approximately 12 houses on it. He would like to survey at least 120 houses before making a conclusion.
Which of the following is an example of random cluster sampling in Kevin's neighborhood?
Kevin could divide his neighborhood into five homogeneous groups and choose one group at random to survey houses within
Kevin could survey every third house in his neighborhood
Kevin could survey five houses at random on every single street in his neighborhood
Kevin could number each house from 1 to 300 and then randomly select 120 houses to survey using a random number generator
Kevin could divide his neighborhood into five different groups and select 25 houses at random from each group to survey
Explanation
In order for cluster sampling to be present, the entire population must be divided into homogeneous groups (known as clusters). For sampling purposes in this problem, clusters must be chosen as a simple random sample. There is only one answer choice that fits this pattern.
Which of the following is the best way to ensure a sample is representative and unbiased?
Take a random sample
Take a census
Take a voluntary response sample
Take a convenience sample
None of the other answers
Explanation
Taking a random sample is the only data-collecting method that ensures that every set of individuals has an equal chance of being selected for the sample and does not introduce any significant bias. Taking either a voluntary response sample or a convenience sample does not ensure these important aspects, as there is some unwanted selectivity involved in the data being collected. Taking a census is inferior to taking a sample of any sort, as it is both costly and time-consuming.
Based on the histogram, which of the following sets of values was most common in the sample?
62-68
58-64
66-72
64-70
54-60
Explanation
You can see from the histogram that the two most frequent ranges for values are 62-64 and 64-66, with 5 values in each group. And from the answer choices, you should see that only one choice, 62-68, contains both of the high-frequency bars. It also contains the next-highest bar (66-68, with a total of 4), so at 14 total values the range 62-68 has the highest frequency of any of these six-inch-range sets in the choices.
Based on the histogram, which of the following sets of values was most common in the sample?
62-68
58-64
66-72
64-70
54-60
Explanation
You can see from the histogram that the two most frequent ranges for values are 62-64 and 64-66, with 5 values in each group. And from the answer choices, you should see that only one choice, 62-68, contains both of the high-frequency bars. It also contains the next-highest bar (66-68, with a total of 4), so at 14 total values the range 62-68 has the highest frequency of any of these six-inch-range sets in the choices.
Your AP Statistics teacher asks you to conduct a survey to determine the most popular cereal brand at your high school. Which of the following should be the survey population in your study?
All students in your high school
Students in your AP Statistics Class
Students in your grade level
All high school students in your city
All high school students in the United States
Explanation
Since your teacher has asked that you determine the most popular cereal brand at your high school, the survey population should be limited to only your high school. Other students' preferences of cereal brands around the nation will have no impact on the survey results.
Additionally, surveying only students in your AP Statistics class or only students in a particular grade level would not be representative of all students in your high school. Therefore, the correct survey population is all students in your high school.
Alpha Corporation developed a new pill to treat elevated glucose levels. They want to test the efficiency of the pill to lower glucose levels by gathering a sample of people with high glucose and giving them either:
-
A daily dose of their new pill ("Experimental Group")
-
A daily placebo pill that looks the same but does not do anything ("Placebo Group")
How can they make this a "Blind Study"?
Randomly sort people into the Experimental or Placebo groups, without letting them know which pill they received.
Give all participants both pills.
Give the pill to people with high blood glucose and low blood glucose.
Keep the participant identities hidden from the experimenters permanently.
Blindfold the participants while they take the pills.
Explanation
A blind experiment is one in which the participant does not know which experimental group they are in-- which is accomplished by not letting them know if they are in the Experimental or Placebo group.
Alpha Corporation developed a new pill to treat elevated glucose levels. They want to test the efficiency of the pill to lower glucose levels by gathering a sample of people with high glucose and giving them either:
-
A daily dose of their new pill ("Experimental Group")
-
A daily placebo pill that looks the same but does not do anything ("Placebo Group")
How can they make this a "Blind Study"?
Randomly sort people into the Experimental or Placebo groups, without letting them know which pill they received.
Give all participants both pills.
Give the pill to people with high blood glucose and low blood glucose.
Keep the participant identities hidden from the experimenters permanently.
Blindfold the participants while they take the pills.
Explanation
A blind experiment is one in which the participant does not know which experimental group they are in-- which is accomplished by not letting them know if they are in the Experimental or Placebo group.
Your AP Statistics teacher asks you to conduct a survey to determine the most popular cereal brand at your high school. Which of the following should be the survey population in your study?
All students in your high school
Students in your AP Statistics Class
Students in your grade level
All high school students in your city
All high school students in the United States
Explanation
Since your teacher has asked that you determine the most popular cereal brand at your high school, the survey population should be limited to only your high school. Other students' preferences of cereal brands around the nation will have no impact on the survey results.
Additionally, surveying only students in your AP Statistics class or only students in a particular grade level would not be representative of all students in your high school. Therefore, the correct survey population is all students in your high school.
Which of the following is the best way to ensure a sample is representative and unbiased?
Take a random sample
Take a census
Take a voluntary response sample
Take a convenience sample
None of the other answers
Explanation
Taking a random sample is the only data-collecting method that ensures that every set of individuals has an equal chance of being selected for the sample and does not introduce any significant bias. Taking either a voluntary response sample or a convenience sample does not ensure these important aspects, as there is some unwanted selectivity involved in the data being collected. Taking a census is inferior to taking a sample of any sort, as it is both costly and time-consuming.
Kevin would like to find out what type of car is the most popular among residents in his neighborhood. There are 25 streets in his neighborhood and each street has approximately 12 houses on it. He would like to survey at least 120 houses before making a conclusion.
Which of the following is an example of random cluster sampling in Kevin's neighborhood?
Kevin could divide his neighborhood into five homogeneous groups and choose one group at random to survey houses within
Kevin could survey every third house in his neighborhood
Kevin could survey five houses at random on every single street in his neighborhood
Kevin could number each house from 1 to 300 and then randomly select 120 houses to survey using a random number generator
Kevin could divide his neighborhood into five different groups and select 25 houses at random from each group to survey
Explanation
In order for cluster sampling to be present, the entire population must be divided into homogeneous groups (known as clusters). For sampling purposes in this problem, clusters must be chosen as a simple random sample. There is only one answer choice that fits this pattern.