The following video will help you with the homework multiple-choice Ch 16 & 20 One-sample t confidence intervals.

Review of three different standard deviations

Standard deviation is a key concept in statistics. As a matter of fact, most of our formulas involve some kind of standard deviations. Here are the three standard deviations that we have encountered since the beginning of this semester:

• • • population standard deviation
    • sample standard deviation
    • standard deviation of the sampling distribution of the sample mean

The video below explains the similarity and difference between the three different standard deviations:

Standard deviations in 3 different contexts

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We have a (relatively) short video today!

We will continue with Ch 21. Our focus is on constructing confidence intervals to estimate difference between two population means.

Instructions

• There are 2 confidence interval problems in this lab work (not from the book).
• • For the 2nd question, follow the format below for the conclusion:

We are 99% confident that the population mean ______ for _____

is smaller than that of _____

               by an amount that might be as small as ………

or is larger than that of _____

              by an amount that might be as large as…….. .

• The video explains the concept and shows you how to do the lab work:

Ch 21 Two-sample confidence interval

• Submit your lab work as one single PDF file to Canvas before the due date.

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In the real world, it is common to compare two responses in statistical studies. For example, comparing the effectiveness of two marketing strategies or two medical treatments.

We can use hypothesis tests or confidence intervals to compare two population means. That’s the subject matter of Ch 21.

Today, we’ll discuss how to compare two population means via hypothesis testing. All the 5 steps are more or less similar to those in one-sample hypothesis tests in Ch 20.

Instructions

• There are 2 problem in this lab work.

• • #21.49 — one-sided hypothesis test
    • The question is exactly the same in both the 8th and the 9th edition.

• • One additional question (not in book) — one-sided hypothesis test

We will do two-sided tests in homework multiple choice problems later.

• The video explains the concept and shows you how to do the lab work:

Ch 21 Two-sample t test

• Submit your lab work as one single PDF file to Canvas before the due date.

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We will continue with confidence intervals today. The calculation on confidence intervals is straightforward — the formula in the box on p455. However, the reasoning behind confidence intervals requires some thinking. The more you understand, the less you have to memorize. Try to understand as much as you can today. When you do multiple choice next week, you will have another opportunity to revisit the concepts at a deeper level. (See bottom of this page for more details).

Instructions

• There is 1 problem, #20.28, with three sub-parts in this lab work. Two of the sub-parts are NOT in the book.  (#20.28 is EXACTLY the same in both the 8th and the 9th edition).

• • #20.28 a) on p472
  • 2 additional sub-parts (1 & 2) based on #20.28

• The video explains the concept and shows you how to do the lab work:

Ch 16 & 20 One-sample t confidence interval

• Submit your lab work as one single PDF file to Canvas before the due date.

For Ch 16 & 20 one-sample t confidence interval multiple-choice questions

The following video is for the multiple choice questions. You don’t need the video below for your lab work today.

Ch 16 & 20 multiple choice — one-sample t confidence interval

Challenge

At this time of the semester, the challenge for students is that they find the concepts and calculations of hypothesis testing and confidence intervals similar and yet different.

When we learn each topic one at a time, things seem straightforward. However, when you put everything together, things start to get confusing.

For example, you might wonder, “How many different ways do we use the t values for?” or “What is the difference between all these standard deviations?”

Questions like these are what we call “connecting the dots”-type of questions. These questions require you to reflect on knowledge from various topics and assimilate them in a coherent manner.

Being able to assimilate knowledge is the key to success in this course. So how do you assimilate concepts?

Focus on homework multiple choice questions!

First, you need to learn the basic concepts well. That means that you aim to score at least 90% in each multiple choice set.

Lab work problems are typically straightforward because that is the first round of learning so the questions cannot be too difficult. But we need to go deeper than the lab work problems and it is where the multiple choice homework comes in.

Some of you may have already noticed that multiple choice homework forms the backbone of each exam (the ideas of lab work problems are already incorporated into each multiple choice set). So if you made mistakes in the multiple choice homework, make sure you go over the mistakes right away instead of waiting till the exam time.

Second, you need to allocate time to think about these “connecting the dots”- type of questions — write down your questions as you go along, reflect and find answers to them! If you have questions, please ask!

Third, practice, practice, practice in the right way! Math is like a sport — the more you practice, the better you play but you have to practice in the right away!

To prepare for the final exam, you are expected to redo each set of multiple choice problems at least two rounds WITHOUT referring to your book or notes. That is, you are expected to memorize the formulas and concepts AFTER you understand them well. If you still make mistakes or need to refer to your book or notes when you are redoing the multiple choice each time, that means you are not ready yet and that means you’ll need to go over the problems one more round. Does it take time? Yes, it does. But there is just no other way to do well in a math class except practice, practice, practice in the right way!

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There are 2 types of statistical inference:

• hypothesis tests
• confidence intervals

We finished one type of hypothesis tests last time — one-sample t test. There are other types of hypothesis tests such as two-sample t tests, etc. But we will take a short break from hypothesis tests and start confidence intervals today.

Instructions

• There are 3 problems in this lab work. The problems are not in the book.

• • 2 problems (z* critical value)
    • For #2, notice that the single tail area of 0.5 lies exactly halfway between 0.0495 and 0.0505. Therefore our z* critical value should also be halfway between z = 1.64 and z = 1.65. That is, z* = 1.645.
• • 1 problem (t* critical value)

• The video explains the concept and shows you how to do the lab work:

Ch 16 & 20 Confidence Intervals

• Submit your lab work as one single PDF file to Canvas before the due date.

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Focus of today

For the past few lessons, we have learned the various components of a hypothesis test but today, we are finally ready to put together all the components and go through the procedure of conducting a hypothesis test from beginning to end.

There are various types of hypothesis tests. The simplest one is the “one-sample t test” in Ch 20, which is the focus of today.

Again, you can find the concepts in Ch 17 and the actual calculations in Ch 20.

Specifically,

— Ch 17 introduces concepts such as hypotheses, P-value and significance level, etc.

— Ch 20 shows how to use the t probability distributions to calculate a t test statistic and finding the corresponding P-value

Instructions

• There are 2 problems in this lab work. The problems are not in the book.

• • 1 hypothesis test problem (one-sided / one-sample t test)
  • 1 hypothesis test problem (two-sided / one-sample t test)

• The video explains the concept and shows you how to do the lab work:

Ch 17 & 20 – one-sample t test

• Submit your lab work as one single PDF file to Canvas before the due date.

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Ch 17 and Ch 20 go hand-in-hand. They are both about hypothesis testing, the bread-and-butter of statistics. Ch 17 is more about concepts while Ch 20 is about calculations.

Instructions

• There is 3 problems in this lab work. None of them is in the book.
  • 2 problems on the t probability distributions
  • 1 problem on finding the t test statistic and tail probability

• The video explains the concept and shows you how to do the lab work:

Ch 17 cont’d and Ch 20

• Submit your lab work as one single PDF file to Canvas before the due date.

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We will go over one more important topic in Ch 15. Then we start Ch 17, the first chapter in statistical reference.

Instructions

• There are 5 problems in this lab work (they are all relatively short):

• • The following lab work question is exactly the same in both the 8th and the 9th edition. The only difference is the question number:

• • • • In the 8th edition, it is #15.31 (In the 9th edition, it is #15.33): —
        • • In this question, we interpret tail probability.

• • #17.2 a) and b) from the 9th edition — reasoning of hypothesis testing

• • 3 questions not in the book — setting hypotheses

• The video explains the concept and shows you how to do the lab work:

Ch 15 (tail probability) & Ch 17

• Submit your lab work as one single PDF file to Canvas before the due date.

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We will continue with Ch 15 today.

At beginning of the video, we introduce the “big picture” type of issues that will become the focus of the 2nd part of the course, statistical inference (Ch 16, 17, 20 and 21). If you find that a bit abstract, don’t worry. We will go over those issues again.

The most important thing to learn today is to calculate probabilities regarding sample means. The techniques will be useful for the rest of the course.

Now, the techniques in this chapter are similar to those in Ch 3 , which makes it somewhat easier to learn. However, this similarity also causes confusion for many students. Just remember this — Ch 3 is about individual observations \( x \) while Ch 15 is about sample means \( \overline{x} \).

Instructions

• There is one problem in this lab work — this lab work question is exactly the same in both the 8th and the 9th edition.  The only difference is the question number:

• • In the 8th edition, it is #15.31  (In the 9th edition, it is #15.33).

• The video explains the concept and shows you how to do the lab work:

Ch 15 cont’d

• Submit your lab work as one single PDF file to Canvas before the due date.

That’s all for today’s lab work.

For Ch 15 multiple choice questions

The following video is for Ch 15 multiple choice questions. You don’t need the video below for your lab work today.

Ch15 mean and SD in different contexts

Several multiple choice homework questions in Ch 15 ask you to differentiate between the three different standard deviations:

• • population standard deviation
  • sample standard deviation
  • standard deviation of the sampling distribution of the sample mean

The video helps to explain all this.

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We will finish Ch 3 and start Ch 15 today.

Ch 15 is one of the most important chapters in this course. The subject materials are more abstract than the previous chapters. So be patient. Pause and take frequent breaks!

Instructions

• There are 2 problems in this lab work (from the 9th edition):

• • #3.36 — find a value given a proportion

• • #15.7 — we use the data but not the sub-parts

• The videos explain the concepts and shows you how to do the lab work:

Ch 3 The Normal Distributions — cont’d — reverse calculations

Ch 15 Sampling distributions

• Submit your lab work as one single PDF file to Canvas before the due date.

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We will continue with Ch 3 today. We will also reacquaint with our old friend, the standardized value. But this time, our old friend looks a bit different.

The types of calculations in this chapter will be used for the rest of the course. So if you have questions, ask!

Instructions

• There are 2 problems in this lab work (there is a slight difference in the numbers between the 8th and the 9th edition for #3.10.  We will use the 9th edition.  See the video for details)
  • #3.10 — part a), b) and c ) (skip part d)
  • #3.12 — part a) only

• The video explains the concepts and shows you how to do the lab work:

Ch 3 The Normal Distributions— cont’d

• Submit your lab work as one single PDF file to Canvas before the due date.

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Ch 3 is one of the three probability chapters in this course (Ch 3, 12 & 15).

In Ch 3 we focus on one special shape of density curve — the bell-shaped. The bell-shaped density curves are the bread-and-butter of probability and statistics.

Instructions

• Here are 2 problems in this lab work: (For the following problems, we are using the 9th edition of the book.  See the video for details.)
  • #3.6
  • #3.7

• The video explains the concepts and shows you how to do the lab work:

Ch 3 The Normal Distributions

• Submit your lab work as one single PDF file to Canvas before the due date.

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We will continue with Ch 12 today. The new concept for this lesson is “random variables.” We will focus on “discrete“ random variables first, then “continuous“ random variables.  Continuous random variables are the bread-and-butter of probability and statistics, an essential tool for the rest of this course!

You will notice that the math is not difficult in this chapter (addition and subtraction). As a matter of fact, the math is not difficult in this course —it’s the concepts and how you apply the concepts that can be challenging.

Instructions

• There is 2 problems in this lab work:
  • #12.45

• • • Note: For #12.45c), in describing the event \( X \leq 2 \) in words, you need to say what X is in plain English (no math notation or symbol). So your answer should be:

The event “\( X \leq 2 \) ” means that “the number of …………. is ……”.

You will NOT get full credits if your answer is missing the words “the number of …….“ because those words represent the meaning of X.

• • problem not in book (uniform probability distribution)

• The videos explain the concepts and show you how to do the lab work:

Ch 12 cont’d — discrete random variables

Ch 12 cont’d — continuous random variables

• Submit your lab work as one single PDF file to Canvas before the due date.

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We will start Ch 12 Introducing Probability.

Starting from Ch 12, we switch from merely exploring data (Ch 1, 2, 4 & 5) to drawing or conclusions about the data that we gather. The process of drawing conclusions based on the data is called statistical inference.

You will notice that things start to get more abstract (the most abstract chapter is Ch 15).

Probability is a abstract and difficult topic. However, we will focus on the basics.

Instructions

There is 3 problems in this lab work:

• • problem not in book (the idea of probability)

• • problem not in book (construct a probability model)
    • You MUST show what the total sum of the probabilities is.
    • Take 4 decimal places for each probability number. Due to round-off errors, the total sum of the probabilities might not be exactly equal to 1 e.g. your sum might be 0.98. That’s OK. But you MUST write out what that sum is equal to.

• • #12.10  (Use the numbers shown in the video, which is the 9th edition)

• The video explains the concepts and shows you how to do the lab work:

Ch 12 Introducing Probability — Rules

• Submit your lab work as one single PDF file to Canvas before the due date.

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We will finish Ch 4 today and start Ch 5 right away. Ch 4 and 5 are closely related.

Today’s videos are a bit long. You might want to take frequent breaks while you are watching. Also, you can fast-forward the last 17 minutes —just make sure you watch the segment Fact 4) for the lab work.  Fact 4) starts at the timestamp 37:56.

Ch 5 is the last chapter in Part I of the book. We have covered four chapters in Part I:  Ch 1, 2, 4, & 5. Part I is about exploring data, which is the most straightforward part of the course.

After Ch 5, we will begin Ch 12 next time but not today.  From Ch 12 onward, you will find the subject matter a bit more abstract. So just keep up with the pace of the class, ask questions and join a study group!

Building on the foundations in Ch 4, we will learn how to do simple predictions in Ch 5, a very practical topic.

Instructions

• There are altogether 5 problems in this lab work:

• • problem not in book (scatterplot with 4 quadrants)
  • #4.23 (Facts about correlation)
  • problem not in book (straight line and slope)
  • problem not in book (calculate squared residuals)
  • #5.38 (linear regression)
    • Think carefully about which variable is explanatory.  Then put the explanatory variable on the x-axis.  How do you know which one is explanatory? The hint is given in b).
    • To do c), you need to know the concept of r-squared. See Fact 4) starting at the timestamp 37:56.

• The two videos explain the concepts and also shows you how to do the lab work:

Ch 4 cont’d and Ch 5

Ch 5 cont’d

• Here is how your grader grades your lab work:

https://www.course.cafe/math/lesson/grading-scheme-for-lab-work-problems/

• Submit your lab work as a single PDF file to Canvas before the due date.

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Motivation

Who doesn’t want to do predictions?! Who doesn’t want to know the future?!

If you ask me,

“Olivia, if I am going to study 2 hours for the exam, can you predict what score I am going to get?”

Wouldn’t it be GREAT if I could give you the exact answer right away based on the exact information that you give me (2 hours of study)?

Unfortunately, so many factors are at play in real life that it is often very difficult to have accurate predictions based on just a handful of factors. Nonetheless, the inherent difficulties haven’t stopped statisticians from trying.

We will learn how to describe and summarize the relationship between two quantitative variables in Ch 4. Then in Ch 5, we will do simple statistical predictions. Ch 4 and Ch 5 are closely related.

Instructions

• There are altogether 3 problems in this lab work:

Note:

If the video requires that you use graphing paper for a certain problem, then you need to use graphing paper to receive full credits. You can use both a “physical” copy of a graphing paper or a “digital” copy of a graphing paper (see below).  Either way, just scan your work as usual as one single PDF.

You can download free graphing paper of various grid sizes from the web. Then you can print it out and use it for your lab work. Here is the graphing paper of 0.25″ grid size: 0.25_inches

• • #4.2 (explanatory vs response variable)
  • #4.27 a) (drawing a scatterplot and describing the relationship)
    • • When you calculate the mean of x and mean of y, don’t round off too soon. Otherwise, your answer for the Extra-subpart won’t be accurate!
  • problem not in book (calculate r)

• The video explains the concepts and also shows you how to do the lab work:

Ch 4  Scatterplots & Correlation

• Submit your lab work as a PDF file to Canvas before the due date.

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We will continue our discussion on measuring the spread of distributions.

“Spread” is a very important concept in statistics. There are various ways to measure how spread out your data are. Many of the concepts and calculations introduced in this chapter will be used throughout the entire semester!

• There are altogether 3 problems in this lab work:

• • #2.13 (side-by-side boxplots)

• • problem not in book (calculate variance, standard deviation)

• • problem not in book (comparing the spread from dotplots )
    • • There is an error in the video: there are 5 (not 4) observations in the data set. So you need to divide the sum by 5 (not 4). My apologies.

• The video listed below explains the concepts and also shows you how to do the lab work:

Ch 2 measuring spread — 5-number summary, boxplots, standard deviation

• Submit your lab work as a PDF file to Canvas before the due date.

• Here is how your grader grades your lab work:

https://www.course.cafe/math/lesson/grading-scheme-for-lab-work-problems/

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How’s your first week of school so far? Hope it is going well.

Today we will start on Ch 2.

Ch 2 is an important chapter in this course. Many of the concepts in this chapter will be used throughout the entire course.

Ch 2 is quite a long chapter. It is slightly more mathematical (more formulas) than the first chapter. Having said that, to do well in this course, you need both the math and the concepts!

Similar to what you did on the 1st day of class, you will:

— Watch the video below and follow the format shown in the video to attempt your lab work before class

— Attend class meeting to participate in class discussion on this set of lab work problems and ask your questions.

— Then fix your errors and submit the lab work by the due date and time.

Here are the detailed Instructions:

• The video listed below explains the concepts and also shows you how to do the lab work. This is a relatively long video. So remember, don’t watch the entire video in one shot. Instead, watch and pause, watch and pause:

Ch 2 — mean, median & quartiles

• There are altogether 3 problems in this lab work.

(As I mentioned in class, there is not much difference between the 8th (old) and the 9th (new) edition of the textbook.  So just follow the questions shown in the video.)

• • Question #1 — not in book (compare mean and median)
  • Question #2 — not in book (draw a dotplot)
  • Question #3 — not in book (find quartiles)

• Here is the Hint to Question 1d) —

Hint_demo_Question1d

• Make sure you follow the format shown in the video as that is how your grader grades your lab work.

• No need to type your lab work. Just write out your lab work on a piece of paper by hand, scan all the pages, save them as one single PDF file and upload your one single PDF file into Canvas by the due date. (You can also type your work on a tablet and then upload your PDF to Canvas.)

• Here is Ch 1 from the 8th edition (there is not much difference between the 8th and the 9th edition).  Nonetheless, I won’t be able to keep posting the entire chapters because of copyright rule.  Hopefully, the library will have a reserved copy of the textbook so that at minimum, you can access that copy.  As I said in class, students tend to do better if they have a digital or physical copy of the textbook on hand.

MA 101 Ch2

• Here is how your grader grades your lab work:

https://www.course.cafe/math/lesson/grading-scheme-for-lab-work-problems/

• We will go over the lab work problems in class.

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Welcome to Ch 1!

On the first day of class (1/25), we will start with Ch 1.

Math is a hands-on subject. To learn math, we need to practice while we learn!

Here is what you need to do:

— Watch the videos listed below and follow the instructions in the videos to do your lab work problems (lab work problems are math exercises related to the materials covered in the videos). You might not be sure about certain details but it’s OK as you can ask questions during the class meeting.  Just make sure you at least “attempt” as much as you could on the lab work problems before you come to class.

— Attend the 1st class meeting to participate in class discussion about the lab work problems. Ask your questions!

— After class, fix the errors, if any, of your lab work problems and then submit your lab work to Canvas by the due date.

Here are the detailed Instructions:

• The videos listed below explain the concepts and also show you how to do the lab work:

Ch 1 (categorical variables)

Ch 1 (quantitative variables)

• Here are the lab work problems due on the first day of class (1/25):
  • • Ch 1—#1.1 (identify individuals and variables)
    • Ch 1—#1.2 (categorical and quantitative variables)
    • Ch 1—#1.4 (bar graph) (see my comments below regarding #1.4a)
    • Ch 1—#1.6 (histogram)
    • problem not in book (dotplot)
      

The first video demonstrates lab work #1.1, #1.2 and #1.4; the second video #1.6 and the dotplot problem.

• Notice that #1.1 and #1.4 are different — #1.1 shows you the entire data set while #1.4 shows you a summary because the question says “The survey reports the following data on the sources …..” For #1.4, the individuals are NOT family sources.

• For #1.4a), to receive full credits, you need to specifically say whether the percentages add up to (or exceed or below) 100%. Just one sentence will do.  Here is the format to follow:

“It is incorrect to use a pie chart of these data because

               the percentages of students  (add up / do NOT add up)  to 100%.”

• In case you are waiting for your textbook, here is Ch 1 from your textbook.   Please note that due to copyright issues, at most, we can post only Ch 1 and 2 — so you need to purchase your textbook or have access to the textbook!!!
  

MA 101 Ch1 revised

• Make sure you follow the format shown in the videos as that is how your grader grades your lab work.

• No need to type your lab work:

• • Write out your lab work on paper by hand (you can also write it on your tablet if you wish).

• • Scan all your pages as one single PDF file.

• • Upload your one single PDF file to Canvas by the due date.
    • Your one-single PDF should have all five lab work problems.

• • After uploading your one single PDF into Canvas, if you realize that you have made mistakes and want to revise your homework, you can upload another PDF into Canvas before the due date. Canvas will keep track of all your submissions and display your latest submission to the grader. In other words, you can submit as many times as you want before the due date!

• • Your homework will NOT be accepted if it is NOT a single PDF file.

• • The library has machines that you can scan for free.

• Here is how your grader grades your lab work:

https://www.course.cafe/math/lesson/grading-scheme-for-lab-work-problems/

• Lab work is typically straightforward as this is the first round of learning. The multiple-choice homework questions that you will do next week will be more challenging than the lab work.

• If you have questions regarding lab work, come to the class meeting and ask!

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