One thousand Florida residents were asked if they would elect the republican or democratic candidate for Governor in the next election. 540 out of 1000 responded that they would vote for the Democratic candidate. Which of the following statements correctly describes how the confidence interval for the population proportion of people that would vote for the democratic candidate should be computed?

A. There are not 15 successes and 15 failures. A confidence interval can not be done.

B. There are not 15 successes and 15 failures. A confidence interval can be computed by adding 2 successes and 2 failures.

C. There are not 15 successes and 15 failures. A confidence interval can be computed by adding 4 successes and 5 failures.

D. There are at least 15 successes and 15 failures. A large sample confidence interval for the population proportion can be computed (phat + / - z * sqrt (p * (1-p) / n) with no additional values added.

Question

Gregory Marsh

Social Studies

11 May, 06:56

One thousand Florida residents were asked if they would elect the republican or democratic candidate for Governor in the next election. 540 out of 1000 responded that they would vote for the Democratic candidate. Which of the following statements correctly describes how the confidence interval for the population proportion of people that would vote for the democratic candidate should be computed?

A. There are not 15 successes and 15 failures. A confidence interval can not be done.

B. There are not 15 successes and 15 failures. A confidence interval can be computed by adding 2 successes and 2 failures.

C. There are not 15 successes and 15 failures. A confidence interval can be computed by adding 4 successes and 5 failures.

D. There are at least 15 successes and 15 failures. A large sample confidence interval for the population proportion can be computed (phat + / - z * sqrt (p * (1-p) / n) with no additional values added.

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Answers (1)

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Lilianna Austin · Answer 1

(D) There are at least 15 successes and 15 failures.

A large sample confidence interval for the population proportion can be computed (p + / - z*sqrt (p * (1-p) / n)) with no additional values added.

Explanation:

The confidence interval for the population proportion of people that would vote for the democratic candidate should be computed as follows:

Confidence interval = p + / - margin of error

p is sample proportion

margin of error is given as z*sqrt[p (1-p) : n]

z is the test statistic

n is the sample size

The lower limit of the sample proportion is computed by subtracting the margin of error from the sample proportion.

The upper limit of the sample proportion is computed by adding the margin of error to the sample proportion.