Search in book...
Toggle Font Controls
Create new playlist

Name your new playlist

Playlist description (optional)
Sign In

Email address

Password

Forgot Password?

or

Continue with Facebook

Continue with Google
Sign Up

Full Name

Email address

Confirm Email Address

Password

or

Continue with Facebook

Continue with Google

Appendix B. Formulas

Many formulas are given on the AP Statistics Exam. The first section of this appendix provides the formulas that you will be given during the AP Exam. The second section of this appendix is a summary of formulas not given on the AP Exam. You should be familiar with the formulas that will be given on the exam (but there’s no need to memorize them). You will probably not use all of the formulas that are given. In fact, you may never use a few of them in the entire course. You should also know and understand all of the formulas in the second section of this appendix, because those will not be given to you on the exam. Knowing the formulas that will not be on the exam will put you at ease when solving problems and will let you focus on answering the questions and doing so in context. Also notice that some of the formulas given on the exam will help you remember the formulas that are not on the exam.

Formulas Given on the AP Exam

The following formulas for Descriptive Statistics, Probability, and Inferential Statistics are given on the AP Statistics Exam:

Descriptive Statistics

$Descriptive Statistics$

Probability

$Probability$

The following formulas are given and should be used if X has a binomial distribution with parameters n and p:

$Probability$

If $Probability$ is the mean of a random sample of size n from an infinite population with mean μ and standard deviation σ, then:

$Probability$

Inferential Statistics

$Inferential Statistics$
Confidence interval: statistic ± (critical value) $Inferential Statistics$ (std. deviation of statis)

*Single-Sample*
Statistic	Standard Deviation of Statistic
Sample mean	$Inferential Statistics$
Sample proportion	$Inferential Statistics$
Two-Sample
Difference of sample means	$Inferential Statistics$
Difference of sample means
(Special case when σ₁ = σ₂)	$Inferential Statistics$
Difference of sample proportions	$Inferential Statistics$
Difference of sample proportion
(Special case when p₁ = p₂)	$Inferential Statistics$
Chi-square test statistic	$Inferential Statistics$

Formulas Not Given on the AP Exam

The following formulas are not given on the AP Exam. Be sure to know and understand how they work and how to apply them.

Normal Distribution

For normal distributions, use
z-score
$Normal Distribution$

Probability

Probability that any two events A and B happen together:
P(A ∩ B) = P(A) $Probability$ P(B / A)
Notice that this formula is given on the AP Exam, but in the following form:
$Probability$
Probability that two independent events A and B happen together:
P(A ∩ B) = P(A) $Probability$ P(B)
General addition rule for the union of two events:
P(A ∪ B) = P(A) + P(B) – P(A ∩ B)
Note that ∪ (union) means “or” and ∩ (intersection) means “and.”
If the events A and B are disjoint (mutually exclusive):
P(A ∪ B) = P(A) + P(B)
Rules for means and variances of random variables for fixed numbers a and b:
μ_z = a ± bμ_x
σ_z² = b²σ_x²
σ_z = bσ_x
Addition rule for variances if X and Y are independent random variables:
σ²_X+Y = σ²_X + σ²_Y
(This is not a typo! We always add variances!)
σ²_X−Y = σ²_X + σ²_Y

Binomial distribution formula:
$Probability$
Notice that the formula for the binomial distribution is given on the AP Exam. It’s given in this section again to ensure that you understand the notation correctly.
Geometric distribution formulas
The probability that the first success is obtained on the nth observation:
P(X = n) = (1 – p)ⁿ⁻¹ p
Probability that it takes more than n trials to obtain the first success:
P(X > n) = (1 – p)ⁿ
Formulas for the mean and standard deviation of a geometric distribution:
$Probability$
Central limit theorem
The central limit theorem says that as the sample size increases, the mean of the sampling distribution of $Probability$ approaches a normal distribution with mean, μ, and standard deviation,
$Probability$
Standard error
When using s to estimate σ, the standard deviation of the sampling distribution for means is $Probability$ When using s to estimate σ, the standard deviation of the sampling distribution is called the standard error of the sample mean, $Probability$ .

Inferential Statistics

The following formulas are used for inferential statistics:

Mean(s)

One sample t-interval:
$Mean(s)$ with n−1 degrees of freedom
One sample t-test:
$Mean(s)$ with n−1 degrees of freedom
Two sample t-interval:
$Mean(s)$
The t^* value depends on the particular level
of confidence that you want and on the degrees of freedom (df).
Two sample t-test:
$Mean(s)$

Proportion(s)

Standard deviation of the sampling distribution of $Proportion(s)$ :
$Proportion(s)$
When dealing with confidence intervals, we do not know p. Because $Proportion(s)$ is an unbiased estimator of p, we use $Proportion(s)$ to estimate p. These two values should be close in value, provided that the sample is large enough. We can then use the standard error of $Proportion(s)$ :
$Proportion(s)$
One-proportion z-interval:
$Proportion(s)$
One-proportion z-test:
$Proportion(s)$
Note that p₀ is the value of the proportion in the null hypothesis.
Two-proportion z-interval:
$Proportion(s)$
When dealing with a confidence interval, the values of p₁ and p₂ are unknown. For this reason, we use the standard error of the statistic $Proportion(s)$ ₁ − $Proportion(s)$ ₂ :
$Proportion(s)$
Two-proportion z-test:
$Proportion(s)$
Use the pooled sample proportion when using a two-proportion test. To find the pooled sample proportion, we use:
$Proportion(s)$

Regression

Mean of all responses of a linear relationship with x that represents the true regression line:
μ = α + βx
Standard error about the regression line:
$Regression$
or
$Regression$
Confidence interval for the true slope (β) of the regression line:
b ± t*SE_b
where SE_b is the standard error of the slope. We can find SE_b by using the following formula:
$Regression$