Applet Exercise The population corresponding to the upper

Chapter 7, Problem 4E

(choose chapter or problem)

Applet Exercise The population corresponding to the upper face observed on a single toss of a balanced die is such that all six possible values are equally likely. Would the results analogous to those obtained in Exercises 7.1 and 7.2 be observed if the die was not balanced? Access the applet DiceSample and scroll down to the part of the screen dealing with “Loaded Die.”

If the die is loaded, the six possible outcomes are not equally likely. What are the probabilities associated with each outcome? Click on the buttons “1 roll,” “10 rolls,” and/or “1000 rolls” until you have a good idea of the probabilities associated with the values 1, 2, 3, 4, 5, and 6. What is the general shape of the histogram that you obtained?Click the button “Show Stats” to see the true values of the probabilities of the six possible values. If Y is the random variable denoting the number of spots on the uppermost face, what is the value for \(\mu=E(Y)\)? What is the value of \(\sigma\) the standard deviation of Y ? [Hint: These values appear on the “Stat Report” screen.]How many times did you simulate rolling the die in part (a)? How do the mean and standard deviation of the values that you simulated compare to the true values

 \(\mu=E(Y) \text { and } \sigma\)? Simulate 2000 more rolls and answer the same question.

Scroll down to the portion of the screen labeled “Rolling 3 Loaded Dice.” Click the button

         “Roll 1000 Sets” until you have generated 3000 observed values for the random

 variable  \(\bar{Y}\)

        I. What is the general shape of the simulated sampling distribution that you obtained?

        II. How does the mean of the 3000 values

 \(\bar{y}_{1} \bar{y}_{2}, \ldots, \bar{y}_{300}\) compare to the value of

\(\mu=E(Y)\) computed in part (a)?How does the standard deviation of the 3000 values compare to \(\sigma / \sqrt{3}\)?

Equation Transcription:

 

   

    

        

 

   

Text Transcription:

\mu=E(Y)

\sigma

\mu=E(Y)  and  \sigma

\bar Y

\bar y_1 \bar y_ 2, \ldots, \bar y_ 300

\mu=E(Y)

\sigma / \sqrt 3