Question

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.

Answer 1

Answer:

(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.

Answer 2

Option D is the correct answer because, with no extra numbers, a broad sample confidence interval for the population proportion can be generated $(p$ +/- $z^{(p\text{ x }(1-p)/n)}$$)$. So,  "there are at least 15 successes and 15 failures."

How to calculate the confidence interval?

The following is the population proportion of persons who would vote for the democratic candidate:

Confidence interval = p +/- margin of error

p = sample proportion

Margin of error = $Z^{[p(1-p)/n]}$

z = test statistic

n = sample size

Subtracting or less the margin of error from the sample proportion yields the lower limit of the sample proportion.

The sample proportion's upper limit is calculated by adding the margin of error to the sample proportion.

For more information about confidence intervals, refer below

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