# Advanced Placement Exam: Trivia Questions On Statistics! Quiz

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Questions: 5 | Attempts: 591  Settings  This quiz is an Advanced Placement Exam, Trivia Questions on Statistics! It is perfect for every student who wants to refresh their understanding on the majorly tested topics. Do you think you know enough to pass it or do you need some more help? Give the quiz a try and keep a look out for other quizzes like it!

• 1.

### Data were collected on two variables X and Y and a least-squares regression line was fitted to the data. The estimated equation for this data is y = -2.29 + 1.70x. One point has x = 5 and y = 6. What is the residual for this point?

• A.

7.91

• B.

6.21

• C.

0.21

• D.

-0.21

• E.

-2.91

D. -0.21
Explanation
The residual for a data point is the difference between the actual value of the dependent variable (y) and the predicted value of the dependent variable based on the regression line. In this case, the estimated equation is y = -2.29 + 1.70x. Plugging in x = 5, we can calculate the predicted value of y as follows: y = -2.29 + 1.70(5) = -2.29 + 8.50 = 6.21. Since the actual value of y is given as 6, the residual is calculated as 6 - 6.21 = -0.21. Therefore, the correct answer is -0.21.

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• 2.

### In a clinic, 50 patients with sleep disorders are randomly assigned to one of two different groups.  Patients in one group are given medication before bedtime.  Patients in another group are given blindfolds and played soft music at bedtime.  Each patient is attached to a machine that records breathing patterns.  From the patterns, it is possible to determine if the patient is awake or asleep.  The data will be used to decide which method is more effective in helping patients with sleep disorders.  Which of the following statements is correct in the context of this experiment?

• A.

This is a double blind experiment because the patients were divided into the two treatment groups randomly.

• B.

It is not possible for this experiment to be single-blind or double-blind, because human subjects are involved.

• C.

This is only a single-blind experiment because the experimenters did not include a control group that received neither medication nor a blindfold and soft music.

• D.

This is only a single-blind experiment because patients will know which treatment they are receiving, although the examining doctor might not.

• E.

This is a double-blind experiment because the experimenters could prevent both groups of patients from knowing what sort of treatment the other group is receiving.

D. This is only a single-blind experiment because patients will know which treatment they are receiving, although the examining doctor might not.
Explanation
In a single-blind experiment, the participants are aware of the treatment they are receiving, but the experimenters are not. In this case, the patients will know whether they are receiving medication or blindfolds and soft music, but the examining doctor may not be aware of the treatment. Therefore, this experiment can be classified as a single-blind experiment.

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• 3.

### In which of the following situations is a binomial model not an appropriate model to describe the outcome?

• A.

The number of heads in three tosses of a coin.

• B.

The number of rainy days in a given week.

• C.

The number of girls in a randomly selected family of five children.

• D.

The number of students over five feet tall at a randomly selected middle school.

• E.

The number of defective computer parts randomly selected from an assembly line.

B. The number of rainy days in a given week.
Explanation
A binomial model is not appropriate to describe the outcome of the number of rainy days in a given week because the number of rainy days in a week is not a fixed number of trials with two possible outcomes (rainy or not rainy). It is a continuous variable that can take on any value from 0 to 7, depending on the weather conditions. Therefore, a binomial model, which is used for discrete variables with a fixed number of trials and two possible outcomes, is not suitable in this situation.

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• 4.

• A.

A

• B.

B

• C.

C

• D.

D

• E.

E

D. D
• 5.

### Two random variables, X and Y, are independent.  X has an expected value 2.5 and a standard deviation 0.3, while Y has an expected value 4.7 and standard deviation 0.4.  Which of the following is true?

• A.

The mean of X + Y is 6.2.

• B.

The standard deviation of X + Y is 0.7.

• C.

The variance of X + Y is 0.7.

• D.

The standard deviation of X - Y = 0.1

• E.

The standard deviation of X - Y = 0.5

E. The standard deviation of X - Y = 0.5
Explanation
Since X and Y are independent random variables, the standard deviation of their difference (X - Y) is equal to the square root of the sum of their variances. Given that X has a standard deviation of 0.3 and Y has a standard deviation of 0.4, the standard deviation of X - Y can be calculated as follows:

Standard deviation of X - Y = sqrt(0.3^2 + 0.4^2) = sqrt(0.09 + 0.16) = sqrt(0.25) = 0.5

Therefore, the standard deviation of X - Y is indeed 0.5.

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