Concept explainers
(a)
To calculate: The
(a)
Answer to Problem 42E
The required probability is 0.1446.
Explanation of Solution
Given information:
Percent of students = 67%
Number of students = 15,000
Number of students for SRS = 100
Number of students who support a crackdown = 62
Formula used:
The mean of the sampling distribution of
The standard deviation of the sampling distribution of
Calculation:
Here,
Find the mean of sampling distribution of
Substitute 62 for x and 100 for n in the above formula
For the mean of the sampling distribution of
Substitute 0.67 for p in the formula
For the standard deviation of the sampling distribution, use the formula
Substitute 0.67 for p and 100 for n in the above formula and simplify.
Now, we find the z-score by using the formula
Substitute 0.62 for
We can find the probability by using table A as:
Hence, the required probability is 0.1446.
(b)
To determine: The explanation that why the survey does not support the conclusion.
(b)
Explanation of Solution
Given information:
Percent of students = 67%
Number of students = 15,000
Number of students for SRS = 100
Number of students who support a crackdown = 62
Formula used:
The mean of the sampling distribution of
The standard deviation of the sampling distribution of
Explanation:
Here,
Find the mean of sampling distribution of
Substitute 62 for x and 100 for n in the above formula
For the mean of the sampling distribution of
Substitute 0.67 for p in the formula
For the standard deviation of the sampling distribution, use the formula
Substitute 0.67 for p and 100 for n in the above formula and simplify.
Now, we find the z-score by using the formula
Substitute 0.62 for
We can find the probability by using table A as:
Thus, the probability is 0.1446.
The above probability is greater than 0.05.
If the true population proportion is 0.67, then a sample can be obtained with sample proportion of 0.62 because the probability is greater than 0.05.
Hence, it is concluded that the survey does not support the conclusion.
Chapter 7 Solutions
The Practice of Statistics for AP - 4th Edition
Additional Math Textbook Solutions
Statistics: The Art and Science of Learning from Data (4th Edition)
Introductory Statistics (10th Edition)
Elementary Statistics (13th Edition)
Statistics for Psychology
Essentials of Statistics (6th Edition)
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