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Each question needs to be 75-150 words 4 questions

1.

In the textbook, §1.8 discusses “Ethical Guidelines for Statistical Practice” and promotes the idea that we should strive to be ethical in all that we do.

  • Why is it important to use statistics ethically?
  • Give an example of unethical use of statistics and explain why it is unethical.
  • Could this unethical use of statistics be corrected so that the statistics are performed fair, thoroughly, and objectively? Why or why not?



2.

1. What is the textbook’s definition of probability?

2. If there are 3 green marbles and 4 red marbles in a bag, and you were asked to draw one without looking, what is the probability of drawing one green marble?

3. If you don’t put that marble back, what is the probability of drawing another green marble?

4. What is the textbook’s definition of conditional probability?

5. Using the above “marbles in the bag” scenario, what is a conditional probability question that you can make from it?

In §4.4 we are introduced to the concept of conditional probability. The notation P(A | B) denotes the probability of event A occurring given that we know event B has occurred.

Now consider the Monty Hall Problem introduced in the following video:

https://m.youtube.com/watch?v=4Lb-6rxZxx0

6. After watching this video, we know that if we are given the option to switch doors that, probabilistically speaking, it is in our best interest to switch. Why is the probability of winning NOT 50/50 when the contestant is given the opportunity to switch?


3.

In §6.2 we are introduced to the Normal Probability Distribution and the special case of the Normal Probability Distribution, the Standard Normal Probability Distribution, which is a Normal Probability Distribution with mean (u) zero and variance (σ2) one (and standard deviation of 1).

Watch these videos

https://www.youtube.com/watch?v=mFYvUxOO2T4

https://www.youtube.com/watch?v=uAxyI_XfqXk

1. What is a z score?

2. What is the purpose of a z score?

3. If a z score were -3, where on the graph would it be? Is this a rare or a common score? Why?

One way to find probabilities from a Standard Normal Distribution is to use probability tables, which are located inside the front cover of your textbook.

4. According to the table, what is the probability when z ≤ -1.23? The probability when z ≤ 1.23?

5. Select two other pairs of “opposites” on the z table (like 2, -2 etc.) and give their probabilities.

6. Show the math of adding each of the pairs. What is the total each time? Why is that the total?

7. What are the properties of the Standard Normal Probability Distribution?

4.

Watch this video: https://www.youtube.com/watch?v=rBjft49MAO8

Go to the link: http://www.random.org/dice/ (or any other online dice rolling link)

Roll the 2 virtual dice and calculate the sum of the pair of virtual dice. Do this 10 times. List your rolls. Show your calculations.

Then after you have rolled the virtual pair dice 10 times and calculated 10 sums, calculate the average of these 10 sums. Show your calculations.

Conduct this experiment again, but this time roll the virtual pair of dice 20 times. Calculate the 20 sums, and then find the average of these 20 sums. Show your work.

How does these exercises relate to this week’s lesson, particularly the Central Limit Theorem?

If we took everyone’s averages for the 20 rolls, and made a histogram, what would we expect to see, and why?

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