AP Statistics : AP Statistics

Study concepts, example questions & explanations for AP Statistics

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Example Questions

Example Question #1 : How To Find Correlation

Which of the following shows the least correlation between two variables? 

Possible Answers:

Correct answer:

Explanation:

The strength of correlation is measured on an absolute value scale of  to  with  being the least correlated and  being the most correlated. The positive or negative in front of the correlation integer simply determines whether or not there is a positive or negative correlation between the variables. 

A correlation of  means that there is no correlation at all between two variables.

Example Question #1 : How To Find Correlation

Which of the following correlation coefficients implies the strongest relationship between variables:

 

 

 

 

Possible Answers:

Correct answer:

Explanation:

A high correlation coefficient regardless of sign implies a stronger relationship. In this case  has a stronger negative relationship than the positive relationship described by a value of 

Example Question #261 : Ap Statistics

A national study on cell phone use found the following correlations:

-The correlation between the number of texts sent each day and a person's average credit card debt is .

-The correlation between the number of texts sent each day and the number of books read each month is .

Which of the following statements are true?

i. As the number of texts sent each day increases, average credit card debt increases.

ii. Sending more texts causes people to read less.

iii. A person's average credit card debt is related more strongly to the number of texts sent each day than the number of books read each month is related to the number of texts sent each day.

 

Possible Answers:

iii

i and iii

ii and iii

i and ii

ii

Correct answer:

i and iii

Explanation:

i is correct because there is a positive correlation between the number of texts sent each day and average credit card debt. 

ii is incorrect because the word "cause" was used in the statement. Correlation does not mean causation. There is a relationship between the number of texts sent each day and the number of books that a person reads each month. However, the number of texts sent each day does not cause a person to read a certain number of books each month. 

iii is correct because the absolute values of the correlations indicate which correlation is stronger.  is a stronger correlation than .

Example Question #1 : How To Find Linearity

A basketball coach wants to determine if a player's height can predict the number of points the player scores in a season. Which statistical test should the coach conduct?

Possible Answers:

Correlation

ANOVA

P-score

T-test

Linear regression

Correct answer:

Linear regression

Explanation:

Linear regression is the best option for determining whether the value of one variable predicts the value of a second variable.  Since that is exactly what the coach is trying to do, he should use linear regression.

Example Question #1 : How To Find The Least Squares Regression Line

In a regression analysis, the y-variable should be the ___________ variable, and the x-variable should be the ___________ variable.

Possible Answers:

Dependent, Independent

Qualified, Unqualified

Independent, Dependent

Greater, Lesser

First, Second

Correct answer:

Dependent, Independent

Explanation:

Regression tests seek to determine one variable's ability to predict another variable.  In this analysis, one variable is dependent (the one predicted), and the other is independent (the variable that predicts).  Therefore, the dependent variable is the y-variable and the independent variable is the x-variable.

Example Question #2 : How To Find The Least Squares Regression Line

If a data set has a perfect negative linear correlation, has a slope of  and an explanatory variable standard deviation of , what is the standard deviation of the response variable?

Possible Answers:

Correct answer:

Explanation:

The key here is to utilize

.

"Perfect negative linear correlation" means , while the rest of the problem indicates  and . This enables us to solve for .



Example Question #3 : Bivariate Data

A least-squares regression line has equation  and a correlation of . It is also known that . What is 

Possible Answers:

Correct answer:

Explanation:

Use the formula .

Plug in the given values for and and this becomes an algebra problem.

 

Example Question #1 : How To Find Outliers

Use the following five number summary to determine if there are any outliers in the data set:

Minimum: 

Q1: 

Median: 

Q3: 

Maximum: 

Possible Answers:

It is not possible to determine if there are outliers based on the information given.

There is at least one outlier on the high end of the distribution and no outliers on the low end of the distribution.

There is at least one outlier on the high end of the distribution and at least one outlier on the low end of the distribution.

There is at least one outlier on the low end of the distribution and no outliers on the high end of the distribution.

There are no outliers.

Correct answer:

There are no outliers.

Explanation:

An observation is an outlier if it falls more than  above the upper quartile or more than  below the lower quartile.

. The minimum value is  so there are no outliers in the low end of the distribution.

. The maximum value is  so there are no outliers in the high end of the distribution.

Example Question #1 : How To Find Outliers

For a data set, the first quartile is , the third quartile is and the median is .

Based on this information, a new observation can be considered an outlier if it is greater than what?

Possible Answers:

Correct answer:

Explanation:

Use the  criteria:

This states that anything less than  or greater than  will be an outlier.

Thus, we want to find

  where .

Therefore, any new observation greater than 115 can be considered an outlier.

Example Question #61 : Data

You are given the following information regarding a particular data set:

Q1: 

Q3: 

Assume that the numbers  and  are in the data set. How many of these numbers are outliers? 

Possible Answers:

One

Four

Three

None of the numbers are outliers

Two

Correct answer:

Two

Explanation:

In order to find the outliers, we can use the  and  formulas.

Only two numbers are outside of the calculated range and therefore are outliers:  and .

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