Question

Suppose that a survey was taken of 32 people and each person was asked if they approved or disapproved of the president's actions during the government shutdown. Nineteen people said that they approved. Which of the following statements correctly describes how the confidence interval for the population proportion of people that approved the President's actions during the government shutdown? Group of answer choices There are not 15 observed successes and 15 observed failures. A confidence interval can not be done. There are not 15 observed successes and 15 observed failures. A confidence interval can be computed by adding 2 successes and 2 failures. There are not 15 observed successes and 15 observed failures. A confidence interval can be computed by adding 4 successes and 5 failures. There are at least 15 observed successes and 15 observed 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:

Option c

Step-by-step explanation:

--The large-sample confidence interval

formula for proportions is valid if np ≥ 15 and n(1-p) ≥ 15. The large sample confidence

interval only contain the true value a certain percentage of the time. A 95% CI will contain the

value 95% of the time. You add 2 successes and 2 failures.

Answer 2

Using confidence interval concepts, the correct option is:

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

In a sample with a number n of people surveyed with a probability of a success of , and a confidence level of , as long as there are at least 15 successes and 15 failures, that is, and , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the z-score that has a p-value of $\frac{1+\alpha}{2}$.

In this problem:

• 19 people approved, thus, 19 successes.
• 32 - 19 = 13 people disapproved, thus, 13 failures.
• 2 extra failures are needed for the confidence interval, thus, the correct option is:

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

A similar problem is given at https://brainly.com/question/15243414