AP Statistics : AP Statistics
Study concepts, example questions & explanations for AP Statistics
All AP Statistics Resources
Example Questions
Example Question #2 : How To Do Cluster Sampling
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 number each house from 1 to 300 and then randomly select 120 houses to survey using a random number generator
Kevin could survey five houses at random on every single street in his 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 divide his neighborhood into five different groups and select 25 houses at random from each group to survey
Kevin could divide his neighborhood into five homogeneous groups and choose one group at random to survey houses within
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.
Example Question #11 : Data Sets And Z Scores
There are four suspects in a police line-up, and one of them committed a robbery. The suspect is described as "abnormally tall". In this case, "abnormally" refers to a height at least two standard deviations away from the average height. Their heights are converted into the following z-scores:
Suspect 1: 2.3
Suspect 2: 1.2
Suspect 3: 0.2
Suspect 4: -1.2.
Which of the following suspects committed the crime?
Suspect 1
Suspect 4
Suspect 2
Suspect 3
Suspect 1
Z-scores describe how many standard deviations a given observation is from the mean observation. Suspect 1's z-score is greater than two, which means that his height is at least two standard deviations greater than the average height and thus, based on the description, Suspect 1 is the culprit.
Example Question #1 : How To Find Descriptive Data From A Z Score
A value has a 
the same as the population mean
below the population mean
above the population mean
two standard deviations from the population mean
one standard deviation from the population mean
below the population mean
The 
Example Question #2 : How To Find Descriptive Data From A Z Score
All of the students at a high school are given an entrance exam at the beginning of 9th grade. The scores on the exam have a mean of 
The z-score equation is 
To solve for 
Example Question #12 : Data Sets And Z Scores
Your professor gave back the mean and standard deviation of your class's scores on the last exam.
Your friend says the z-score of her exam is 
What did she score on her exam?
The z-score is the number of standard deviations above the mean.
We can use the following equation and solve for x.
Two standard deviations above 75 is 85.
Example Question #11 : Data Sets And Z Scores
Your boss gave back the mean and standard deviation of your team's sales over the last month.
Your friend says the z-score of her number of sales is 
How many sales did she make?
The z-score is the number of standard deviations above or below the mean.
We can use the known information with the following formula to solve for x.
Example Question #3 : How To Find Descriptive Data From A Z Score
The following data set represents Mr. Marigold's students' scores on the final. The standard deviation for this data set is 8.41. If you scored 0.91 standard deviations worse than the mean, what was your score?
To work with a z-score, first we need to find the mean of the data set. By adding together and dividing by 26, we get 81.15.
We know that your score is 0.91 standard deviations WORSE than the mean, which means that your z-score is -0.91. We can use the following formula for the z-score:
where z is the z-score, x is your data point, 
multiply both sides by 8.41
Example Question #12 : Data Sets And Z Scores
Your teacher gives you the z-score of your recent test, and says that the mean score was a 60, with a standard deviation of 6. Your z-score was a -2.5. What did you score on the test?
To find out your score 
As such,
So you scored a 
Example Question #1 : How To Conduct An Observational Study
You are conducting the following series of observational studies to determine if generally understood parameters about a local population are accurate:
A. You stand on the sidewalk next to a stop sign to observe and record the number of cyclists and drivers who stop or don't stop.
B. You inform customers at a local fast food restaurant of your study to determine the proportion of healthy food choices from the menu and then observe their choices.
C. From your car in the mall parking lot, you observe the proportion of shoppers who hold the door open for the next person who enters or exits the mall.
D. To estimate the proportion of males and females in the local community, you observe spectators at a hockey match and count and record the gender in a randomly selected area of the crowd.
E. You review the daily sign-in sheets at a local fitness center to estimate the average number of workouts per week for residents of the local community.
Which observational study should yield the most accurate results?
Study A
Study D
Study B
Study E
Study C
Study C
Study C takes a representative sample of local residents, and it does so without affecting the outcomes.
Studies A and B are influenced by the person conducting the survey. Studies D and E are biased samples of the population.
Therefore, C should yield the most accurate results.
Example Question #1 : Census And Studies
What situation would most warrant the method of observational study to produce accurate results?
Testing the effectiveness of a new drug.
Studying the social interactions between groups of baboons.
Observing how chocolate consumption affects mood.
Studying the relationship between sleep deprivation and cold susceptibility.
None of the above.
Studying the social interactions between groups of baboons.
Obseverational study does not involve any interference with the group being studied, so watching baboons in their natural habit would be best suited for this method.
Certified Tutor
All AP Statistics Resources
