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32nd International Conference on Technology in Collegiate Mathematics

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VIRTUAL CONFERENCE

32nd International Conference on Technology in Collegiate Mathematics VIRTUAL CONFERENCE

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A Different Approach to Homework in The Introductory Statistics Course

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Student Anxiety

• Empirical evidence has

shown that many students face anxiety about the Introductory Statistics even before day one.

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Student Difficulty With Homework

• Students need

homework that shows them how to solve problems step by step. No hints. No ‘read section 4.5 in the textbook.’

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Student Difficulty With Homework

• Students need

homework that grades them for doing homework not for the percent that they have answered correct.

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Students Need Many and Varied Resources

• Resources should

include Powerpoints that do not look like pages from a book but rather include images and have animated slides showing one at a time step by step solutions to student

• riented word

problems.

32nd International Conference on Technology in Collegiate Mathematics VIRTUAL CONFERENCE

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Students Need Many and Varied Resources

• An additional resource

are many YouTube videos carefully chosen to include those from a varied pool of different articulate, easy to follow instructors.

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Students Need Many and Varied Resources

Require a Videos Journal from

• students. They create

transcripts of problems solved in each video. Collect the journal the day of a test and ‘skim’ through them. To encourage watching the videos I usually give students 100%.

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My 911 Suite Will Address Some of The Issues

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The Only Non-Online Statistics Software

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Coming Soon: Chi Square

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Common Intro Stat Topics

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Unique Features of STAT911 Tutorial Software

• Not online. No WIFI needed.
• Runs off a USB Flash Drive
• Never Expires
• No Install needed
• Always different random

Problems

• Step by step solutions
• 10 minute learning curve
• Plenty of Word Problems
• Includes Corequisite Topics in Context
• Includes Animated Powerpoints
• Crossword Puzzles for Vocabulary
• USE YOUR DATA helps students with

term projects

• Grade Reports are printed by students
• Grade reports are turned in to Professor

STAT911 Tutorial Software can be Used as an Extra Resource With Online Software

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On The Stat911 Menu

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Chapter 2 Graphs

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Chapter 3 Descriptive Measures

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Chapter 4 Probability

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Chapters 5 and 9 Normal Distributions

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Chapter 6 Confidence Intervals

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Chapter 7 Hypothesis Testing

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Chapter 8 Correlation and Regression

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Stat911 Easy Navigation

• Click on Chapter
• Click on Section/Level
• Problem Appears
• Enter Answer OR
• Click on SEE SOLUTION
• Keep Clicking to see all

the steps in the solution

CLICK Sections Will Appear Problems are categorized by chapters, sections, levels of difficulty and different types within levels..

Click on Choice of Level White box

Problem Appears On Top Instructions Appear On Bottom

Put your answer in the White Box or Click the Green Button For the Answer

Answer appears in 2nd White Box Click Green Button ‘See All Steps

Keep clicking Green button To see the rest of the steps. First step appears above with explanation in the white Box at the bottom

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Use Your Data Great for Projects

Students enter their own data to get Descriptive Measures, Correlation Coefficients, Confidence Intervals, Hypothesis Test Decisions, and much more !

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Students Enter Data and Get Graphs. Great for their projects

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Let’s Look At More Menu Form Buttons.

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Sample Turned In Grade Report

• Red X means, that level had no problems
• Grades are color coded
• Stat911 uses ‘Mastery Learning.’
• Wrong answers do not count.
• Students always do homework because 100% is achievable.
• Students always turn in reports because of peer pressure.

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Stat911 Powerpoints

• Animated Slides
• Dozens of Word

Problems Explained

• All with step by step

solutions

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Powerpoints With plenty of examples with step by step solutions

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Powerpoint By Professor Martin Weissman

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Find The 2 Hypothesis Problem #1

We have a medicine that is being manufactured and the pills are supposed to average 12 milligrams of the active ingredient.

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Find The 2 Hypothesis Problem #1

H0: μ ≤ 12 H0: μ ≥ 12 H0: μ = 12 H1: μ ≠ 12 H1: μ > 12 H1: μ < 12

We have a medicine that is being manufactured and their pills are supposed to average 12 milligrams of the active ingredient.

Which set of Hypotheses would you start the Hypothesis Test With?

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Find The 2 Hypothesis Problem #1

H0: μ ≤ 12 H0: μ ≥ 12 H0: μ = 12 H1: μ ≠ 12 H1: μ > 12 H1: μ < 12

We have a medicine that is being manufactured and their pills are supposed to average 12 milligrams of the active ingredient. The Claim is average = 12

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Find The 2 Hypothesis Problem #1

H0: μ ≤ 12 H0: μ ≥ 12 H0: μ = 12 H1: μ ≠ 12 H1: μ > 12 H1: μ < 12

We have a medicine that is being manufactured and their pills are supposed to average 12 milligrams of the active ingredient. Claim is Null Hypothesis. It has the equal sign. The Claim is average = 12

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Find The 2 Hypothesis Problem #1

H0: μ ≤ 12 H0: μ ≥ 12 H0: μ = 12 H1: μ ≠ 12 H1: μ > 12 H1: μ < 12

We have a medicine that is being manufactured and their pills are supposed to average 12 milligrams of the active ingredient. Claim is average = 12 Claim is Null Hypothesis. It has the equal sign.

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Find The 2 Hypothesis Problem #1

H0: μ ≤ 12 H0: μ ≥ 12 H0: μ = 12 H1: μ ≠ 12 H1: μ > 12 H1: μ < 12

We have a medicine that is being manufactured and their pills are supposed to average 12 milligrams of the active ingredient. Claim is average = 12 Claim is Null Hypothesis. It has the equal sign. Alternate Hypothesis is average ≠ 12

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Find The 2 Hypothesis Problem #2

A car dealership announces that the mean time for an oil change is less than 15 minutes

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Find The 2 Hypothesis Problem #2

H0: μ ≤ 15 H0: μ ≥ 15 H0: μ = 15 H1: μ ≠ 15 H1: μ > 15 H1: μ < 15

A car dealership announces that the mean time for an oil change is less than 15 minutes

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Find The 2 Hypothesis Problem #3

A company advertises that the mean life of its car batteries is at least 36 months.

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Find The 2 Hypothesis Problem #3

H0: μ ≤ 36 H0: μ ≥ 36 H0: μ = 36 H1: μ ≠ 36 H1: μ > 36

Which set of Hypotheses would you start the Hypothesis Test With?

A company advertises that the mean life of its car batteries is at least 36 months.

H1: μ < 36

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Find The 2 Hypothesis Problem #4

A company claims that its products follow FDA guidelines state a product must contain at most (less than or equal to) 20 parts per million of gluten to qualify as gluten free.

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Find The 2 Hypothesis Problem #4

H0: μ ≤ 20 H0: μ ≥ 20 H0: μ = 20 H1: μ ≠ 20 H1: μ > 20 H1: μ < 20

A company claims that its products follow FDA guidelines state a product must contain at most (less than or equal to) 20 parts per million of gluten to qualify as gluten free.

Which set of Hypotheses would you start the Hypothesis Test With?

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Basics Of Hypothesis Testing

#1 The Area under the Normal Curve is separated into 2 Regions. #2 The 2 Regions are called Reject and Fail To (or Do Not) Reject Regions. #3 The Reject region is ALWAYS a Tail #4 The Reject region pictured above is a RIGHT tail

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Left Tail Test

Right-tail Hypothesis Test Here the test is a Left-tail Hypothesis Test

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Types of Hypothesis Tests

A third type of Hypothesis Testing is with a Two-tail test Right-tail Hypothesis Test Left-tail Hypothesis Test

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H0: μ ≥ 12 H1: μ < 12 H0: μ ≤ 12 H1: μ > 12 a a

Represents critical value

Left or Lower- tail test Right or Upper- tail test Two-tail test

Rejection regions are shaded

/2

a

/2

a H0: μ = 12 H1: μ ≠ 12

Non-rejection region

The 3 types Of Hypotheses Tests

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Example: Calcium in the Diet

Calcium most abundant element in body, and one of the most

• important. Recommended daily

allowance (RDA) for adults is 850 mg/day

Does the data support claim that people below the poverty level have a different calcium intake from RDA?

Random sample of 10 people below poverty level show that From previous study, we know σ = 188 mg

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Example: Calcium in the Diet

1

• Make A Claim

2

• H0 and Ha

3

• Critical Score

4

• Test Score

5

• Reject/Do Not Reject

The null hypothesis is the opposite and has the equality symbol H0: μ = 850 Different means NOT EQUAL TO H1: μ ≠ 850 The Alternative Hypothesis always has the inequality

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Hypothesis Test for Calcium

747.4 850 102.6 1.726 59.45 188/ 10 − − = = = −

• 1.833

+1.833

• 1.726

1

• Make A Claim

2

• H0 and Ha

3

• Critical Score

4

• Test Score

5

• Reject/Do Not Reject

The test statistic falls in the Fail To (Do Not) Reject the Null Hypothesis We do not reject the null hypothesis. The average daily calcium intake is not significantly different for people below the poverty line.

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For the Step By Step Solution just click.

Time To Fill Out A Form

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Time To Fill Out A Form

1

• Make A Claim

2

• H0 and Ha

3

• Critical Score

4

• Test Score

5

• Reject/Do Not Reject

This claim indicates a right one-tail test and is the Alternative Hypothesis. The Alternative hypothesis always has an Inequality. So since the claim is ‘longer or more than’ we have Ha: : μ > 15 The Null Hypothesis ALWAYS has the equal sign and is the

• pposite or complement of the alternative hypothesis.

The Null hypothesis would therefore be H0 : μ ≤ 15

17 5 45 15 .05 x s n

• ne

tail test   = = = = = −

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Time To Fill Out A Form

1

• Make A Claim

2

• H0 and Ha

3

• Critical Score

4

• Test Score

5

• Reject/Do Not Reject

1.65

/ X t s n  − =

17 15 2 2 2.68 5/6.708 0.745 5/ 45 − = = = =

2.68 The test statistic falls in the Reject the Null Hypothesis Region We reject the null hypothesis and accept the Alternative Hypothesis. The average time to fill out the form is significantly longer than 15 minutes. Critical Score

17 5 45 15 .05 x s n

• ne

tail test   = = = = = −

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Click for the Step By Step Solution

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1

• Make A Claim

2

• H0 and Ha

3

• Critical Score

4

• Test Score

5

• Reject/Do Not Reject

This claim “is less than 77’ is the Alternative Hypothesis. The Alternative hypothesis always has an Inequality. So since the claim is ‘is less than’ we have Ha: : μ < 77 The Null Hypothesis ALWAYS has the equal sign and is the opposite

• r complement of the

alternative hypothesis. The Null hypothesis would therefore be H0 : μ ≥ 77

71.4 20.65 20 77 .05 x s n

• ne

tail test   = = = = = −

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Average Life Span In Hawaii

1

• Make A Claim

2

• H0 and Ha

3

• Critical Score

4

• Test Score

5

• Reject/Do Not Reject
• 1.729

/ X t s n  − = 71.4 77 5.6 5.6 1.213 20.65/4.472 4.617 20.65/ 20 − − − = = = = −

• 1.213

.05 20 20 1 19 n df  = = = − =

The test statistic falls in the Fail To (Do Not) Reject the Null Hypothesis We do not reject the null hypothesis The life span of people in Honolulu is NOT significantly less than 77. Critical Score

71.4 20.65 20 77 .05 x s n

• ne

tail test   = = = = = −

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Additional Resources in STAT911

• ‘Use Your Data ‘ great

for term Projects

• Crossword Puzzles To

Learn Terminology

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Stat911 Use Your Data

• Great For Projects

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Use Your Data Great for Projects

Students can enter their data and get Descriptive Measures, Correlation Coefficients, Confidence Intervals, Hypothesis Test Decisions, and much more !

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Enter Your Data Print your graphs Great for rojects

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Stat911 Crossword Puzzles

• Great For Vocabulary

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Contact Information

Name: Martin Weissman Title: Associate Professor Institution: Essex County College 303 University Ave Newark, NJ 07102 Email: weissman@essex.edu