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Get Full Access to Mathematical Statistics With Applications - 7 Edition - Chapter 9 - Problem 14e
Get Full Access to Mathematical Statistics With Applications - 7 Edition - Chapter 9 - Problem 14e

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# Applet Exercise Refer to Exercise 9.13. Scroll down to the ISBN: 9780495110811 47

## Solution for problem 14E Chapter 9

Mathematical Statistics with Applications | 7th Edition

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Problem 14E

Problem 14E

Applet Exercise Refer to Exercise 9.13. Scroll down to the portion of the applet labeled “Mean of Normal Data.” Successive observed values of a standard normal random variable can be generated and used to compute the value of the sample mean . These successive values are then plotted versus the respective sample size to obtain one “sample path.”

a Do you expect the values of to cluster around any particular value? What value?

b If the results of 50 sample paths are plotted, how do you expect the variability of the estimates to change as a function of sample size?

c Click the button “New Sequence” several times. Did you observe what you expected based on your answers to parts (a) and (b)?

Reference

Applet Exercise Refer to Exercises 9.9–9.12. Access the applet Point Estimation.

a Chose a value for p. Click the button “New Sequence” repeatedly. What do you observe?

b Scroll down to the portion of the applet labeled “More Trials.” Choose a value for p and click the button “New Sequence” repeatedly. You will obtain up to 50 sequences, each based on 1000 trials. How does the variability among the estimates change as a function of the sample size? How is this manifested in the display that you obtained?

Reference

Applet Exercise Refer to Exercise 9.11. What happens if each sequence is longer? Scroll down to the portion of the screen labeled “Longer Sequences of Trials.”

a Repeat the instructions in parts (a)–(c) of Exercise 9.11.

b What do you expect to happen if p is not 0.5? Use the button in the lower right corner to change to value of p. Generate several sequences of trials. Comment.

Reference

Applet Exercise Refer to Exercises 9.9 and 9.10. How can the results of several sequences of Bernoulli trials be simultaneously plotted? Access the applet PointbyPoint. Scroll down until you can view all six buttons under the top graph.

a Do not change the value of p from the preset value p = .5. Click the button “One Trial” a few times to verify that you are obtaining a result similar to those obtained in Exercise 9.9. Click the button “5 Trials” until you have generated a total of 50 trials. What is the value of that you obtained at the end of this first sequence of 50 trials?

b Click the button “New Sequence.” The color of your initial graph changes from red to green. Click the button “5 Trials” a few times. What do you observe? Is the graph the same as the one you observed in part (a)? In what sense is it similar?

c Click the button “New Sequence.” Generate a new sequence of 50 trials. Repeat until you have generated five sequences. Are the paths generated by the five sequences identical? In what sense are they similar?

Reference

Applet Exercise Refer to Exercise 9.9. Scroll down to the portion of the screen labeled “Try different probabilities.” Use the button labeled “p =” in the lower right corner of the display to change the value of p to a value other than .5.

a Click the button “One Trial” a few times. What do you observe?

b Click the button “100 Trials” a few times. What do you observe about the values of as the number of trials gets larger?

Reference

Applet Exercise How was Figure 9.1 obtained? Access the applet PointSingle at academic. cengage.com/statistics/wackerly. The top applet will generate a sequence of Bernoulli trials times. How many trials n have you simulated? What value of did you observe? Is the value close to .5, the true value of p? Is the graph a flat horizontal line? Why or why not?

c Click the button “100 Trials” a single time. What do you observe? Click the button “100 Trials” repeatedly until the total number of trials is 1000. Is the graph that you obtained identical to the one given in Figure 9.1? In what sense is it similar to the graph in Figure 9.1?

d Based on the sample of size 1000,what is the value of ? Is this value what you expected to observe?

e Click the button “Reset.” Click the button “100 Trials” ten times to generate another sequence of values for .Comment.

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##### ISBN: 9780495110811

Since the solution to 14E from 9 chapter was answered, more than 270 students have viewed the full step-by-step answer. This textbook survival guide was created for the textbook: Mathematical Statistics with Applications , edition: 7. This full solution covers the following key subjects: trials, button, click, applet, exercise. This expansive textbook survival guide covers 32 chapters, and 3350 solutions. The answer to “Applet Exercise Refer to Exercise 9.13. Scroll down to the portion of the applet labeled “Mean of Normal Data.” Successive observed values of a standard normal random variable can be generated and used to compute the value of the sample mean . These successive values are then plotted versus the respective sample size to obtain one “sample path.”a Do you expect the values of to cluster around any particular value? What value?b If the results of 50 sample paths are plotted, how do you expect the variability of the estimates to change as a function of sample size?c Click the button “New Sequence” several times. Did you observe what you expected based on your answers to parts (a) and (b)?ReferenceApplet Exercise Refer to Exercises 9.9–9.12. Access the applet Point Estimation.a Chose a value for p. Click the button “New Sequence” repeatedly. What do you observe?b Scroll down to the portion of the applet labeled “More Trials.” Choose a value for p and click the button “New Sequence” repeatedly. You will obtain up to 50 sequences, each based on 1000 trials. How does the variability among the estimates change as a function of the sample size? How is this manifested in the display that you obtained?ReferenceApplet Exercise Refer to Exercise 9.11. What happens if each sequence is longer? Scroll down to the portion of the screen labeled “Longer Sequences of Trials.”a Repeat the instructions in parts (a)–(c) of Exercise 9.11.b What do you expect to happen if p is not 0.5? Use the button in the lower right corner to change to value of p. Generate several sequences of trials. Comment.ReferenceApplet Exercise Refer to Exercises 9.9 and 9.10. How can the results of several sequences of Bernoulli trials be simultaneously plotted? Access the applet PointbyPoint. Scroll down until you can view all six buttons under the top graph.a Do not change the value of p from the preset value p = .5. Click the button “One Trial” a few times to verify that you are obtaining a result similar to those obtained in Exercise 9.9. Click the button “5 Trials” until you have generated a total of 50 trials. What is the value of that you obtained at the end of this first sequence of 50 trials?b Click the button “New Sequence.” The color of your initial graph changes from red to green. Click the button “5 Trials” a few times. What do you observe? Is the graph the same as the one you observed in part (a)? In what sense is it similar?c Click the button “New Sequence.” Generate a new sequence of 50 trials. Repeat until you have generated five sequences. Are the paths generated by the five sequences identical? In what sense are they similar?ReferenceApplet Exercise Refer to Exercise 9.9. Scroll down to the portion of the screen labeled “Try different probabilities.” Use the button labeled “p =” in the lower right corner of the display to change the value of p to a value other than .5.a Click the button “One Trial” a few times. What do you observe?b Click the button “100 Trials” a few times. What do you observe about the values of as the number of trials gets larger?ReferenceApplet Exercise How was Figure 9.1 obtained? Access the applet PointSingle at academic. cengage.com/statistics/wackerly. The top applet will generate a sequence of Bernoulli trials times. How many trials n have you simulated? What value of did you observe? Is the value close to .5, the true value of p? Is the graph a flat horizontal line? Why or why not?c Click the button “100 Trials” a single time. What do you observe? Click the button “100 Trials” repeatedly until the total number of trials is 1000. Is the graph that you obtained identical to the one given in Figure 9.1? In what sense is it similar to the graph in Figure 9.1?d Based on the sample of size 1000,what is the value of ? Is this value what you expected to observe?e Click the button “Reset.” Click the button “100 Trials” ten times to generate another sequence of values for .Comment.” is broken down into a number of easy to follow steps, and 685 words. Mathematical Statistics with Applications was written by and is associated to the ISBN: 9780495110811. The full step-by-step solution to problem: 14E from chapter: 9 was answered by , our top Statistics solution expert on 07/18/17, 08:07AM.

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