Concept explainers
(a)
To explain which one will have the larger margin of error.
(a)
Answer to Problem 22E
The class’s interval will be larger since its
Explanation of Solution
It is given in the question that a city ballot includes a local initiative that would legalize gambling. The issue is hotly contested and two groups decide to conduct polls to predict the outcome. Thus, we can say that the class’s interval will be larger since its sample size is smaller.
(b)
To find both confidence interval.
(b)
Answer to Problem 22E
For newspaper:
For class:
Explanation of Solution
It is given in the question that a city ballot includes a local initiative that would legalize gambling. The issue is hotly contested and two groups decide to conduct polls to predict the outcome. Thus, we can say that the class’s interval will be larger since its sample size is smaller. Thus, we have,
Let us first check the conditions for the newspaper as:
Random condition: It is satisfied as it is assumed that the sample is randomly selected.
Normal condition: It is satisfied as,
Thus, all the conditions are met. Therefore, now, to find the confidence interval for newspaper we will use the calculator
Thus, the confidence interval for newspaper will be as:
Now, for the class, first check the conditions as:
Random condition: It is satisfied as it is assumed that the sample is randomly selected.
Normal condition: It is satisfied as,
Thus, all the conditions are met. Therefore, now, to find the confidence interval for class we will use the calculator
Thus, the confidence interval for class will be as:
(c)
To explain which group concludes that the outcome is too close to call and why.
(c)
Answer to Problem 22E
The students group concludes that the outcome is too close to call.
Explanation of Solution
It is given in the question that a city ballot includes a local initiative that would legalize gambling. The issue is hotly contested and two groups decide to conduct polls to predict the outcome. Thus, we can say that the class’s interval will be larger since its sample size is smaller. Thus, the confidence interval for newspaper will be as:
And the confidence interval for class will be as:
So, we can say that the group of students conclude that the outcome is too close to call because
Chapter 19 Solutions
Stats: Modeling the World Nasta Edition Grades 9-12
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