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(a)
To find the margin of error for the 2007 poll if we want 90% confidence in our estimate of the percent of national adults who are baseball fans.
(a)
Answer to Problem 13E
0.025 .
Explanation of Solution
It is given in the question that in a poll taken in March , Gallup asked 1006 national adults whether they were baseball fans or not. Thus, to find the margin of error for the 2007 poll if we want 90% confidence in our estimate of the percent of national adults who are baseball fans, we have,
First find the critical value as:
z*=invNorm(0.95,0,1)=1.645
Then, the margin of error will be:
ME=1.645×√0.36×0.641006=0.025
Thus, 0.025 margin of error for the 2007 poll is needed if we want 90% confidence in our estimate of the percent of national adults who are baseball fans.
(b)
To explain what that margin of error mean.
(b)
Explanation of Solution
It is given in the question that in a poll taken in March , Gallup asked 1006 national adults whether they were baseball fans or not. Then, the margin of error will be:
ME=1.645×√0.36×0.641006=0.025
Thus, 0.025 margin of error for the 2007 poll is needed if we want 90% confidence in our estimate of the percent of national adults who are baseball fans. Thus, the margin of error is the error region about the point estimate.
(c)
To explain would the margin of error be larger or smaller.
(c)
Answer to Problem 13E
The margin of error will be larger.
Explanation of Solution
It is given in the question that in a poll taken in March , Gallup asked 1006 national adults whether they were baseball fans or not. Then, the margin of error will be:
ME=1.645×√0.36×0.641006=0.025
Thus, 0.025 margin of error for the 2007 poll is needed if we want 90% confidence in our estimate of the percent of national adults who are baseball fans. Thus, a 99% confidence level contain a larger range which means that the margin of error must be larger.
(d)
To find that margin of error.
(d)
Answer to Problem 13E
0.039 .
Explanation of Solution
It is given in the question that in a poll taken in March , Gallup asked 1006 national adults whether they were baseball fans or not. Thus, to find the margin of error be larger or smaller, we have,
First find the critical value as:
z*=invNorm(0.995,0,1)=2.576
Then, the margin of error will be:
ME=2.576×√0.36×0.641006=0.039
(e)
To explain will smaller margins of error produce greater or less confidence in the interval.
(e)
Answer to Problem 13E
It will produce less confidence in the interval.
Explanation of Solution
It is given in the question that in a poll taken in March , Gallup asked 1006 national adults whether they were baseball fans or not. Then, the margin of error will be:
ME=2.576×√0.36×0.641006=0.039
Thus, smaller margins of error produce less confidence in the interval because smaller margins of error will mean smaller confidence intervals which occur with decreasing confidence levels.
(f)
To explain do you think there is been a change from 2006 to 2007 in the real proportion of national adults who are baseball fans.
(f)
Answer to Problem 13E
No, there is no change.
Explanation of Solution
It is given in the question that in a poll taken in March , Gallup asked 1006 national adults whether they were baseball fans or not. Then, the margin of error will be:
ME=2.576×√0.36×0.641006=0.039
Thus, we think that there is no change from 2006 to 2007 in the real proportion of national adults who are baseball fans because both proportions belong in the confidence interval (0.321,0.399) .
Chapter 19 Solutions
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