hypothesis definition ap stats

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AP Statistics : Significance

Study concepts, example questions & explanations for ap statistics, all ap statistics resources, example questions, example question #1 : how to do large sample tests of significance for differences between two proportions.

We are comparing the Democratic percentage of Detroit to the Democratic percentage of Dallas. 

In Detroit, we sampled 300 people and 208 were Democrats (.693)

In Dallas, we sampled 350 people and 265 were Democrats (.757)

What is the p-value for the .064 difference?

(Assume a 2-tailed test.)

.0344 is for one tail, so .0688 is for both tails.

(Percentages are different at the .9312 level.)

Example Question #2 : How To Do Large Sample Tests Of Significance For Differences Between Two Proportions

Example question #1 : how to test of significance for the slope of a least squares regression line.

A statistician conducts a regression analysis and obtains a p-value of 0.1. It is more likely than not that there is a relationship between the variables in the study.

A p-value of 0.1 is generally not sufficient to reject the null hypothesis, but this is only because we want a high degree of confidence before finding a relationship between variables.  Here, there is most likely a relationship between the variables even though the statistician could not reject the null hypothesis.

Example Question #1 : Inference

Not enough information to be able to decide.

Any confidence interval can be used to create a hypothesis test by inverting it, and it is fairly simple, but the concept is tested into graduate-level statistics theory.

Example Question #3 : Inference

Which of the following is an incorrect condition requirement for regression inference?

A trend/pattern of some sort in the residual plot

The standard deviation of the response must be constan

Ordered pairs must be independent of each other

All of the following choices are correct conditions except for the choice concerning a trend/pattern of some sort in the residual plot. For regression inference to be accurate, we need to look at the residual plot of the data of interest and make sure there is random scatter. Random scatter indicates that the ordered pairs are indeed independent of each other. Any sort of pattern present in the residual plot would not satisfy that requirement, and therefore would not enable us to successfully use regression inference.

Example Question #2 : Inference

Step 2: This is a one-sided z test because the questions asks if the mean height of boys is greater than the mean height of girls.

Example Question #1 : Defining Errors

Therefore our equation to solve becomes:

Example Question #1 : How To Define A Type Ii Error

You and a classmate wanted to test the effect of sugars and fats on levels of blood sugar.

Your classmate told you that they found the null hypothesis valid, which was what there is no difference between the effects of sugars and fats on blood sugar levels.

If the null hypothesis was actually false, what type of error was made?

Type I and II

A type I error occurs when the null hypothesis is valid but rejected.

A type II error occurs when the null hypothesis is false, but fails to be rejected.

Because the null hypothesis was false, but had failed to be rejected, they made a Type II error.

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Alternative Hypothesis

The alternative hypothesis is a statement that contradicts or negates the null hypothesis. It suggests that there is a significant relationship or difference between variables.

Think of the alternative hypothesis as a detective's theory about a crime. It proposes that something meaningful and important has occurred, just like how the alternative hypothesis suggests there is a significant relationship between variables.

Related terms

Null Hypothesis : A statement that assumes no significant relationship or difference between variables.

Type I Error : When we reject the null hypothesis when it is actually true.

Type II Error : When we fail to reject the null hypothesis when it is actually false.

" Alternative Hypothesis " appears in:

Subjects ( 1 ).

AP Psychology

Study guides ( 5 )

AP Statistics - 6.7 Potential Errors When Performing Tests

AP Statistics - 6.9 Justifying a Claim Based on a Confidence Interval for a Difference of Population Proportions

AP Statistics - 6.10 Setting Up a Test for the Difference of Two Population Proportions

AP Statistics - 7.4 Setting Up a Test for a Population Mean

AP Statistics - 9.5 Carrying Out a Test for the Slope of a Regression Model

Additional resources ( 1 )

AP Statistics - What Are the Best Quizlet Decks for AP Statistics?

Practice Questions ( 5 )

• In a chi-squared test for homogeneity, what does the alternative hypothesis indicate?
• For a chi-square test of independence the alternative hypothesis states:
• What is the alternative hypothesis (Ha) for a t-test of the slope when testing whether the slope is not equal to a hypothesized value (β0)?
• Can we "accept" a null or alternative hypothesis?
• Which of the following is an invalid alternative hypothesis for a one-proportion z-test?

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Sat / act prep online guides and tips, what is (and isn't) on the ap statistics formula sheet.

Advanced Placement (AP)

If you're going to be taking the AP Statistics exam, you're in luck! During the test, you'll have access to a formula sheet that has many useful equations. However, you need to know exactly what's on the AP Statistics formula sheet and how to use it before test day in order for it to be helpful.

In this guide, we go over everything you need to know about the newly-updated AP Stats formula sheet. We'll explain the exact equations that it includes, show you what the formula sheet looks like, go over a few important equations it doesn't contain, and give you tips on how to get the most out of it.

What's on the AP Statistics Formula Sheet?

The AP Stats formula sheet was updated in 2019 to better meet the needs of students during the exam. It's actually two pages of statistics formulas that you'll be given on test day. The formulas will be at the beginning of both the multiple-choice and free-response sections of the test, so you'll have access to them for the entire AP exam. That's great because that means you don't need to memorize any of these formulas!

What's on this AP statistics cheat sheet? You can see exactly what the formula sheet will look like here (beginning on page 261) as well as below.

The formula sheet has three sections: descriptive statistics, probability and distributions, and sampling distributions and inferential statistics. Below are screenshots of the formula sheet, along with a list of the equations it includes.

Descriptive Statistics Formulas

• Sample mean
• Sample standard deviation
• Simple linear regression line
• Regression coefficient
• Sample correlation coefficient

Probability and Distributions Formulas

• Rule of addition
• Rule of multiplication
• Expected value of $X$
• Variance of $X$
• Binomial formula
• Mean of binomial distribution
• Standard deviation of binomial distribution
• Mean of geometric distribution
• Standard deviation of geometric distribution

Sampling Distributions and Inferential Statistics Formulas

• Standardized test statistic
• Confidence interval
• Standard deviation of sample mean
• Standard deviation of proportion
• Standard deviation of difference of sample means
• Standard deviation of difference of sample proportions
• Chi-square test statistic
• Standard error of regression slope
• Mean of sampling distribution of the proportion
• Standard deviation of sampling distribution of the proportion
• Mean of sampling distribution of the mean
• Standard deviation of the sampling distribution of the mean
• Sampling distribution of a sample slope

What Isn't on the AP Statistics Reference Sheet That You Should Know?

The AP Statistics formula sheet contains pretty much all the equations you need to know for the exam, but there are some equations they've left out that may come in handy on test day. Below are the most important of these. Be sure to memorize them because they won't be listed on the AP Stats formula sheet!

Descriptive Statistics

Interquartile range.

The interquartile range, or IQR, is the middle 50% of values when ordered from lowest to highest. The IQR is the difference between the 75th and 25th percentiles, or the first quartile subtracted from the third quartile. The IQR is used to show dispersion, and it can be a useful way to describe the data in boxplots, histograms, scatterplots, etc.

The equation is IQR = Q3-Q1

You can also use IQR to determine if an outlier exists. A commonly used formula is if a data point is more than $\bo 1.5*$ IQR above Q3 or below Q1, then it's an outlier.

The residual ($e$) is the difference between the observed value of the dependent variable (y) and the predicted value ($ŷ$). It's used in regression analysis. Each data point has one residual.

The formula looks like this: $e=y−ŷ$

Both the sum of the residuals and the mean of the residuals are equal to zero, or $Σe=0$ and $e=0$.

Probability

Bayes' theorem.

Bayes' theorem is useful for calculating conditional probabilities. You'll use conditional probability when trying to find the probability of an event given that another event has already occurred.

Conditional probability questions usually follow a format similar to "Given $x$, what is the probability that $y$ occurs?" Use Bayes' theorem to solve them.

Bayes' Theorem: $P(A|B)={P(B|A)*P(A)}/{P(B)}$

Tips for Getting the Most out of the AP Stats Formula Sheet

As you can see, the AP Statistics formula sheet can be very useful during the exam since it helps you avoid memorizing long lists of equations. There are some tips to getting the most out of it though, and we go over the three most important in this section.

#1: Know How to Use the Formulas

It seems like obvious advice, but it's very easy to take a glance at the AP Statistics cheat sheet and move on, knowing you'll have it with you on the test. However, test day is not when you want to be trying to understand what the different formulas mean or how to use them.

If you go into the AP exam not sure of what's on the formula sheet, you'll lose tons of valuable time searching for the right equations and struggling with how to use them properly.

Well before exam day, be sure to go through every formula on the sheet and make sure you understand it and know how to use it.

The College Board includes each of these formulas because they think they're necessary for doing well on the AP Statistics exam, so you should trust them and make sure you know them! If you're not sure how to use some of the equations, here's a helpful site that goes over what each of the formulas is used for.

#2: Know Calculator Shortcuts

You're allowed a graphing calculator for the entire exam, and you should take advantage of some of the nifty things it does. Calculator shortcuts can save you precious time on the test by quickly solving certain AP Statistics equations and finding pieces of data. They also give you a way to check your work for some problems. Stanford has a handy list of calculator shortcuts you can use with your graphing calculator.

There are two caveats though. First, don't become so dependent on your calculator that you forget how to solve the equations on your own or the logic behind them. Second, you should use calculator shortcuts primarily for the multiple-choice section of the test, where you just have to select the correct answer choice.

For the free-response section of the exam, you'll need to show all the work you did for each question, and simply writing which shortcut you plugged into your calculator won't cut it. Use the shortcuts primarily to check your work on free response.

#3: Take Practice Tests With the Formula Sheet

Answering practice questions and taking practice tests using the AP Statistics formula sheet is also key to doing well on the exam. You should take several practice AP tests before the actual exam, and for each of them you should use the official AP Statistics formula sheet. Your teacher will also likely give you a copy of the formula sheet for your in-class exams, so you can get some practice in there too.

If you need help finding practice tests, check out our guide specifically on where to find the best AP Statistics practice questions and tests.

Summary: Using the AP Statistics Formula Sheet

The AP Statistics reference sheet can be a big help during the exam, but only if you already know what's on it and how to use it. The formula sheet is actually three pages that contain useful equations in descriptive statistics, probability, and inferential statistics.

While this AP Statistics cheat sheet doesn't contain everything you need to know, it does include many key AP Statistics equations that you'll need to use on the test.

In order to get the most out of your AP Stats formula sheet, make sure you know all the formulas, pick up some useful calculator shortcuts, and be sure to take some practice tests with the AP Statistics reference sheet.

What's Next?

Looking for more AP Statistics prep? Check out our ultimate guide to the AP Statistics exam to learn everything you need to know to ace the test.

How's your grasp on calculating significance? Brush up on your t-tests and how to calculate statistical significance here .

Practice tests are key to preparing for AP Statistics. Our guide has links to all the best AP Stats practice tests so you can put your formula sheet to use!

How many AP classes should you take? Get your answer based on your interests and your college goals.

Christine graduated from Michigan State University with degrees in Environmental Biology and Geography and received her Master's from Duke University. In high school she scored in the 99th percentile on the SAT and was named a National Merit Finalist. She has taught English and biology in several countries.

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Helping math teachers bring statistics to life

Type 1 and Type 2 Error ( Topic 6.7 )

Chapter 9 - day 9, learning targets.

Interpret a Type I and a Type II error in context. Give a consequence of each error in a given setting.

Activity: Should Rockford Switch to Bottled Water?

Answer Key:

This Activity is based on a  real event that happened in a town  close to the high school where TheStatsMedics teach. Many of our students were aware of the water pollution and this made the lesson relevant for students.

Experience First, Formalize Later

In this Activity, students get to grapple with the potential consequences of using significance tests to make decisions, but without all the formal vocabulary. In the debrief, we formalize the learning by introducing the language of Type 1 and Type 2 errors and also showing them this table:

As a preview of what will come later in Lesson 9.3, you can inform students that the “Correct conclusion” in the top right corner of this table is the power of the significance test. Students always ask what we call the “Correct conclusion” in the lower left of the chart. We tell them that this is the agility of the test (yes, we made this up).

Joint Probability or Conditional Probability

When we start talking about the probability of making a Type 1 or Type 2 error (and later power), it is important to clarify a common misconception. These probabilities are NOT joint probabilities, they are CONDITIONAL probabilities.

Luke's Lesson Notes

Here is a brief video highlighting some key information to help you prepare to teach this lesson.