Discuss how each of the following factors affects the width of the confidence interval for p. (Hint: Consider the confidence interval formula.) (a) the confidence level As the confidence level increases, the interval becomes narrower. As the confidence level increases, the interval becomes wider. (b) the sample size As the sample size increases, the interval becomes wider. As the sample size increases, the interval becomes narrower. (c) the value of p Values of p further from 0.5 give smaller values of ô(1 - p). Therefore, the further the value of ô from 0.5, the wider the interval. Values of p further from 0.5 give smaller values of ①(1 - p). Therefore, the further the value of ô from 0.5, the narrower the interval. Values of p further from 0.5 give larger values of p(1 - p). Therefore, the further the value of ô from 0.5, the wider the interval. Values of p further from 0.5 give larger values of p(1 - p). Therefore, the further the value of ô from 0.5, the narrower the interval.
Discuss how each of the following factors affects the width of the confidence interval for p. (Hint: Consider the confidence interval formula.) (a) the confidence level As the confidence level increases, the interval becomes narrower. As the confidence level increases, the interval becomes wider. (b) the sample size As the sample size increases, the interval becomes wider. As the sample size increases, the interval becomes narrower. (c) the value of p Values of p further from 0.5 give smaller values of ô(1 - p). Therefore, the further the value of ô from 0.5, the wider the interval. Values of p further from 0.5 give smaller values of ①(1 - p). Therefore, the further the value of ô from 0.5, the narrower the interval. Values of p further from 0.5 give larger values of p(1 - p). Therefore, the further the value of ô from 0.5, the wider the interval. Values of p further from 0.5 give larger values of p(1 - p). Therefore, the further the value of ô from 0.5, the narrower the interval.
Chapter9: Sequences, Probability And Counting Theory
Section9.7: Probability
Problem 1SE: What term is used to express the likelihood of an event occurring? Are there restrictions on its...
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Transcribed Image Text:Discuss how each of the following factors affects the width of the confidence interval for p. (Hint: Consider the confidence interval formula.)
(a) the confidence level
As the confidence level increases, the interval becomes narrower.
As the confidence level increases, the interval becomes wider.
(b) the sample size
As the sample size increases, the interval becomes wider.
As the sample size increases, the interval becomes narrower.
(c) the value of p
Values of p further from 0.5 give smaller values of ô(1 - p). Therefore, the further the value of ô from 0.5, the wider the interval.
Values of p further from 0.5 give smaller values of ①(1 - p). Therefore, the further the value of ô from 0.5, the narrower the interval.
Values of p further from 0.5 give larger values of p(1 - p). Therefore, the further the value of ô from 0.5, the wider the interval.
Values of p further from 0.5 give larger values of p(1 - p). Therefore, the further the value of ô from 0.5, the narrower the interval.
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