(a)
To explain what should the theoretical
(a)
Answer to Problem 3E
The theoretical mean for all the sample sizes be
Explanation of Solution
It is given in the question, the responses of the mails are recorded by the organization for different sample sizes. Thus, as given in the question the theoretical mean for all the sample sizes be
Thus, for all the sample sizes it can be calculated as:
(b)
To explain how close are those theoretical values to what was observed in these simulations.
(b)
Answer to Problem 3E
They look very similar in values.
Explanation of Solution
It is given in the question, the responses of the mails are recorded by the organization for different sample sizes. As we see at the table for the observed means and the standard deviation and the theoretical means and the standard deviation as follows:
n | Observed Mean | Theoretical Mean | Observed deviation | Theoretical deviation |
20 | 0.0497 | 0.05 | 0.0479 | 0.0486 |
50 | 0.0516 | 0.05 | 0.0309 | 0.0313 |
100 | 0.0497 | 0.05 | 0.0215 | 0.0217 |
200 | 0.0501 | 0.05 | 0.0152 | 0.0154 |
Thus, by comparing the theoretical vales with the observed values we can see that they seems very similar in values.
(c)
To find out at what
(c)
Answer to Problem 3E
The sample size would you be comfortable using the Normal model as an approximation for the sampling distribution is the sample size of
Explanation of Solution
It is given in the question, the responses of the mails are recorded by the organization for different sample sizes. As we see at the table for the observed means and the standard deviation and the theoretical means and the standard deviation as follows:
n | Observed Mean | Theoretical Mean | Observed deviation | Theoretical deviation |
20 | 0.0497 | 0.05 | 0.0479 | 0.0486 |
50 | 0.0516 | 0.05 | 0.0309 | 0.0313 |
100 | 0.0497 | 0.05 | 0.0215 | 0.0217 |
200 | 0.0501 | 0.05 | 0.0152 | 0.0154 |
Thus, the sample size would you be comfortable using the Normal model as an approximation for the sampling distribution, by looking at the histogram in previous exercise is the sample size of
(d)
To explain what does the success or failure condition say about the choice you made in part (c).
(d)
Explanation of Solution
It is given in the question, the responses of the mails are recorded by the organization for different sample sizes. As we see at the table for the observed means and the standard deviation and the theoretical means and the standard deviation as follows:
n | Observed Mean | Theoretical Mean | Observed deviation | Theoretical deviation |
20 | 0.0497 | 0.05 | 0.0479 | 0.0486 |
50 | 0.0516 | 0.05 | 0.0309 | 0.0313 |
100 | 0.0497 | 0.05 | 0.0215 | 0.0217 |
200 | 0.0501 | 0.05 | 0.0152 | 0.0154 |
Thus, the sample size would you be comfortable using the Normal model as an approximation for the sampling distribution, by looking at the histogram in previous exercise is the sample size of
Thus, it is viable because there are at least ten people for both the successes and failures.
Chapter 18 Solutions
Stats: Modeling the World Nasta Edition Grades 9-12
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