Interactive and Relevant Applications of Statistics

Hawkes statistics courses include games and simulations that help students apply key concepts to the world outside of the classroom. Check these out below! If you’re an instructor who would like to explore these games and simulations yourself, sign up for free student access today.

1. Games of Chance

gamesofchance2

Relevant Application:
This lesson helps students apply the concept of the expected value of a random variable to winning or losing games. Students develop a rational approach to analyzing decisions that involve risk. After all, many business decisions—such as purchasing new equipment, hiring additional employees, and expanding into new markets—involve some kind of risk, and students need to assess these situations as best as they can.

Learn Key Concepts:

  • Basic probability distribution
  • Binomial distribution function
  • Hypergeometric distribution function

2. Direct Mail

directmail2

Relevant Application:
Even in today’s digital world, direct mail marketing remains one of the most viable and proven strategies to connect with customers.

Active Learning Approach:
By assuming the role of a direct mail marketing manager, students start off with $20,000. They are then tasked with developing a strategy by finding mailing lists that will produce sufficient sales, using confidence intervals to determine which lists to use to reach their $40,000 goal.

They win when they correctly formulate which questions they need to solve, collect the data, and analyze the data to evaluate potential risk and profitability for each mailing list.

Learn Key Concepts:
The game provides an environment in which students apply statistical concepts while making business decisions. They also learn the following:

  • Confidence intervals
  • Experimentation
  • Statistical analysis
  • Inference

3. Estimating Population Proportions

estimatingpopulationproportions

Relevant Application:
Students might not realize at first how many decisions involve measurements of a population attribute. For example, television stations base advertising charges on
ratings that reflect the percentage of viewers who watch a particular show. Political analysts are concerned with the fraction of voters who prefer a certain candidate. No
matter the field, estimating population proportions gives us greater insight into the data given to us.

Active Learning Approach:
In the game, students see a box filled with red and blue balls, and are asked to estimate the proportion of red balls in the population. They can draw sample sizes of 20, 50, or
100 to help them estimate the population proportion.

Learn Key Concepts:

  • Determine the minimum sample size for a particular confidence level.
  • Construct a confidence interval for a population proportion.

4. Central Limit Theorem with Proportions

Relevant Application:
In many decisions, the variable of interest is a proportion. A university may want to know the fraction of first-year students with low grades in order to provide more support and resources for them. Manufacturers may be concerned with the fraction of parts that are defective.

Active Learning Approach:
Students see a box of red and blue balls, then draw three samples to calculate the sample proportions for each sample taken. Students draw samples again after being informed that samples of first 20 balls and then 40 balls were drawn 200 times to determine the proportion of the number of red balls to the total number of balls chosen. Students then view the data, including tables and histograms, to understand that the sampling distribution of the sampling proportion is approximately normal.

Learn Key Concepts:
Determine p-hat using the Central Limit Theorem for population proportions.

SIMULATIONS

1. Name That Distribution

namethatdistribution

Relevant Application:
This concept builder strengthens analytical skills in distribution recognition and data analysis. By detecting symmetric or skewed data, students will begin to understand how to apply this knowledge in the real world.

Active Learning Approach:
Students are asked to identify the type of distribution from a given histogram, frequency/relative frequency distribution, statistics table, or set of sample data. They
can increase the number of intervals on the histogram or frequency distribution, view different sample displays, or choose to view a hint before submitting their answer.

Learn Key Concepts:

  • Analyze the histogram, frequency, statistics, and sample data of a distribution.
  • Identify different distribution types: uniform, normal, exponential, chi-square, Poisson, and mystery.

2. Central Limit Theorem

The simulation can run automatically and in bursts. This image shows histograms for n=5, n=15, and n=30. It includes the histogram of the parent function.

Relevant Application:
This simulation shows students how to use samples to make useful predictions about a population. Since many population sizes are too large to have their data collected and analyzed, we turn to the Central Limit Theorem for help.

The visual nature of this simulation lets students truly comprehend how the sample means from any population are normally distributed, regardless of the original
population’s distribution.

Active Learning Approach:
Students select a parent distribution and set the sample sizes and the burst rate. They choose the desired distribution type: exponential, chi-square, normal, Poisson, or bi-modal. Students can decide to run the simulation a set number of times or automatically, which will keep the simulation running.

Learn Key Concepts:

  • Sample population
  • Mean
  • Variance
  • Standard deviation
  • Distribution type

3. Type II Error

You can select the plus or minus buttons for alpha, true mean, and sample size to change the graph. The shaded part increases or decreases depending on the number, and the bell curve moves forward or backward when you change the true mean.

Relevant Application:
Understanding hypothesis testing and type II error is essential to fields like evidence-based medicine, quality engineering, and reliability engineering, among others.

Active Learning Approach:
The variance, hypotheses, and critical values are given. Students can increase or decrease the level of significance (α), true mean (μ), and sample size to see how these
changes affect the other factors involved.

Learn Key Concepts:

  • Examine the interrelationship between α, sample size, and β (the probability of making a type II error).
  • Develop an understanding of the concept of type II errors and the calculation of beta.
  • Explore the relationship between α and β.

 


Are you an instructor who would like to explore these lessons further?

Sign up for FREE student access today!

Additional Questions in Foundations of English Composition

New questions are available in the curriculum for Foundations of English. We’ve expanded the question bank so that you can assign more material related to reading skills and grammar & mechanics. Check out which questions are new below, then assign them using the Assignment Builder in your Hawkes Grade Book!

Lesson Question Serial No.
2.1 11
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2.2 11
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2.3 11
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4.3 21
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4.6 15
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4.7 18
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4.8 12
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4.12 19
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5.6 30

Additional Questions in English Composition

New questions are available in the curriculum for English Composition. We’ve expanded the question bank so that you can assign more material related to different parts of the essay, critical reading & writing skills, and more. Check out which questions are new below, then assign them using the Assignment Builder in your Hawkes Grade Book!

Lesson Question Serial No.
1.1 12
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1.2 11
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1.3 11
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1.4 11
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1.5 11
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1.6 11
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1.7 11
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1.8 11
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1.9 14
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2.1 11
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2.2 11
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2.3 11
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2.4 11
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3.1 11
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3.2 11
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3.3 13
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3.4 11
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3.5 11
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3.6 11
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4.1 11
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4.2 11
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4.3 11
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4.4 11
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4.5 11
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4.6 11
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5.1 11
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5.2 13
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5.3 11
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5.4 6
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5.5 11
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5.6 11
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5.7 11
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5.8 11
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5.9 11
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5.10 11
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6.1 6
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6.2 6
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6.3 11
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6.4 11
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6.6 11
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6.7 11
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6.8 6
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7.1 9
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Upgraded Assignment Reviewer

**COMING SOON**

Soon, you’ll be able to view student grades on both lessons and WebTests, including question statistics, from one centralized location: Assignment Reviewer.

The Assignments tab in the Hawkes Grade Book is shown, with the link to Assignment Reviewer circled.

When you open up Assignment Reviewer, you’ll be able to sort assignments by lessons or WebTests. Each assignment is listed, along with scores.

You can view question statistics to see how much of your class answered each question correctly, helping you assess whether you need to go over certain concepts again in the next class. You can also check out the average time spent on each question, giving you further insight into which concepts students struggle with the most.

When you look at students’ performance at Certifies, you can quickly see who mastered the lesson and who hasn’t, as well as the number of attempts.

When a student attempts a Certify, you can see exactly how they answered each question. Just select their name from the list to see an overall report of the Certify session.

Once you choose the Review Attempt button, you’ll see exactly how the student answered each question. Use the drop-down menu at the top of the page to easily navigate to any questions the student answered incorrectly.

This tool helps you keep track of performance on both individual student and overall class levels. For more information, call us at 1-800-426-9538.

Six ideas to get the most out of your Learn Screen Notes

Customize your lessons even further with the Learn Screen Notes tool, which allows you to add your own content to our pre-created Learn screens. If you want to take full advantage of all that this tool has to offer, try out the six expanded uses below!

1. Embed videos.

Have you uploaded a video to YouTube to help explain a certain concept to students, or love a video that you can share with your class? Easily embed it within the notes.

In YouTube, select the Share option of a video, then copy and paste the code within the Embed area:

The number 1 is next to the Share button of a video in YouTube. The number 2 is next to the Embed button. Below that, the link to the video is highlighted.

Next, when you’re logged into Learn Screen Notes from your Grade Book, select the Source option at the top of the menu. Paste the code into the field. If needed, you can change the width and height of the video. Deselect the Source button.

Hawkes Learning's Learn Screen Notes is shown. Within the menu of formatting and content options at the top, the Source button is selected with the number 1 next to it. Below that, the number 2 is next to the video code that is now pasted within the field. A call-out next to the code says, "Change width and height of video," pointing to the area in the code to do so.

You can then preview what students will see when they log into their courseware and enter the Learn mode:

An example of what the student sees as a Learn Screen Note is shown. Underneath the pre-created objectives slide within a Hawkes lesson, there is a video that the student can click to view.

 

2. Embed Google Docs.

This option is a great way for you to share more in-depth notes that you’ve typed up for class.

**First, make sure your document is uploaded to Google Drive.**

Open Google Site (New > More > Google Site).

Select From Drive, then select the file you wish to embed.

The Google Drive menu is shown with an arrow pointing at the "From Drive" option in the drop-down menu.

Within Google Drive's My Drive, an arrow points at a Word Document underneath the Files category.

Copy and paste the embedded file into Word, and you’ll get a link similar to this:

https://drive.google.com/open?id=0B_5e341lLJGwcXFSYUFCQW9aX28&authuser=0

(The part in red will be unique to the document you select.)

Then, use the following HTML code, replacing what’s in red with the corresponding part in your Google link:

<p><iframe align=”middle” class=”YMEQtf L6cTce-purZT L6cTce-pSzOP” frameborder=”0″ height=”700″ scrolling=”yes” src=”https://drive.google.com/file/d/0B_5e341lLJGwcXFSYUFCQW9aX28/preview?authuser=0″ width=”700″></iframe></p>

In your Learn Screen Notes, select the Source button at the top of the menu, then paste your HTML code. Deselect the Source button, then use Preview to check things out:

A preview of the Hawkes Learning student courseware with the Learn Screen Note is shown. Below the pre-created objectives list within the Learn mode, a Word document is shown.

 

3. Embed interactive elements.

A few instructors we work with have told us about Geogebra and Desmos, which are two websites that let you create interactive graphs and elements. You can share these within your Learn Screen Notes easily!

For Desmos:

After you create your graph, select the Share option at the top of the page. Choose Embed, then copy the code.

A number one is next to the Share button at the top menu. A number two is next to the Embed link underneath "Share your graph," then a number three highlights the HTML code to embed.

In your Learn Screen Notes, select the Source button, paste the link into the notes section, then deselect Source. Choose Preview to see what it looks like for your students:

A Hawkes Learn screen is shown with the lesson slide on the top half of the page and an interactive graph at the bottom.

For Geogebra:

In Geogebra, select the menu option next to the interactive element (the symbol with three dots), then Share. Choose the </> Embed link and copy the code.

In the website Geogebra, a Share box with options to group, link, email, and embed the graph is shown. The Embed option is highlighted above the HTML code.When you’re in your Learn Screen notes, follow the same steps as those for inserting Desmos graphs.

A Hawkes Learn screen is shown with the lesson content at the top of the page and an interactive image of two weights with adjustable masses at the bottom.

 

4. Add images.

If an image is online, you can just copy and paste it into your notes!

If you take a photo of your lecture notes or scan them and save them as an image, you’ll just need to copy and paste it into a Google Doc. Then, copy the image from the Google Doc and paste it into your Learn Screen Notes.

An arrow points at the Copy option from a drop-down menu for an image pasted in a Google Doc.

5. Embed Google Slides.

Add any PowerPoint presentation that you’ve created for class directly into the Hawkes courseware using Google Slides. (And remember Hawkes has PowerPoint presentations available at http://www.hawkeslearning.com/Instructors/InstructorResources.htm!) Just make sure you upload your presentation to your Google Drive, then follow these quick steps:

When you’re in Google Slides, open up the presentation. Select File > Publish to web > Embed. Then, copy the code provided.

A PowerPoint presentation is shown in Google Slides. The "Open with" drop-down menu is displayed, with Google Slides highlighted.A window titled "Publish to the web" is shown. The Embed tab is chosen, and the Publish button is highlighted.

In your Learn Screen Notes…you guessed it! Select Source, paste the code, deselect Source, and then choose Preview to check it out:

A Hawkes Learn screen is shown with the lesson at the top of the page and the PowerPoint presentation at the bottom.

 

6. Embed Google Forms.

Want to add in quick quizzes to check in on students’ progress within Learn, or even polls regarding the lesson content? Now you can using Google Forms!

First, create your Google Form. Select the Send button in the top right, then “< >.” Copy the HTML code.

The Send Form in Google Forms is shown. The Embed HTML is highlighted.

Once you’re in your Learn Screen Notes, follow the usual steps: select Source, paste the code, deselect Source, and then choose Preview.

The Hawkes Learn screen is shown with the lesson content at the top of the page and the embedded Google Form at the bottom. The embedded Google Form is called Pop Quiz and asks a true/false question of "A square has five 90 degree angles."

 


If you have any questions on using Learn Screen Notes, contact your Training & Support Specialist at 1-800-426-9538.

 

Please note that Hawkes Learning is not responsible for user-created content. View our Terms of Use.

Splitter, be gone!

We have a quick interface update in the online student courseware: the splitter is no longer there!

In case you’re unsure of what the splitter looked like, it was the line between the question and answer in Practice and Certify. It could be moved up and down, but doing so was difficult; sometimes it would hide part of the question. Instructors and students informed us of this issue, and we took action.

Before:

A Practice question in Hawkes is shown on the top half of the screen. The bottom half shows a graph where students plot the points to answer the question. In between the question and answer is a dotted line that can be moved up and down.

Now, students only see a clean and simple divider differentiating between the space for question and answer. This change makes our student courseware more accessible and user-friendly for all.

After:

A Practice question in Hawkes is shown on the top half of the screen. The bottom half shows a graph where students plot the points to answer the question. In between the question and answer is just a line, which improves the look and usability of the page.