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## How large a sample is needed if we wish to be 96% confident that our sample proportion in Exercise 9.53 will be within 0.02 of the true frac

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How large a sample is needed if we wish to be 96% confident that our sample proportion in Exercise 9.53 will be within 0.02 of the true fraction of the voting population?

A. A random sample of 200 voters in a town is selected, and 114 are found to support an annexation suit. Find the 96% conﬁdence interval for the fraction of the voting population favoring the suit.

B. What can we assert with 96% conﬁdence about the possible size of our error if we estimate the fraction of voters favoring the annexation suit to be 0.57?

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Mathematics
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2021-08-23T10:30:27+00:00
2021-08-23T10:30:27+00:00 1 Answers
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## Answers ( )

Complete Question

How large a sample is needed if we wish to be 96% confident that our sample proportion in Exercise 9.53 will be within 0.02 of the true fraction of the voting population?

Exercise 9.53A. A random sample of 200 voters in a town is selected, and 114 are found to support an annexation suit. Find the 96% conﬁdence interval for the fraction of the voting population favoring the suit.

B. What can we assert with 96% conﬁdence about the possible size of our error if we estimate the fraction of voters favoring the annexation suit to be 0.57?

Answer:The First questionABThe possible size of our error if we estimate the fraction of voters favoring the annexation suit to be 0.57 is

Step-by-step explanation:From the question we are told that

The margin of error is

The sample size is n = 200

The number that supported the annexation suit is k = 114

Considering the first questionGenerally our sample in Exercise 9.53 is

From the question we are told the confidence level is 96% , hence the level of significance is

=>

Generally from the normal distribution table the critical value of is

Generally the sample size is mathematically represented as

=>

=>

=>

Considering question BGenerally the margin of error is mathematically represented as

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Considering question AGenerally the sample proportion of the number that supported the annexation suit is mathematically represented as

=>

Generally 96% confidence interval is mathematically represented as

=>

=>