Question

Suppose that a Coke/Pepsi survey was conducted of 400 randomly selected individuals from Gainesville. Two hundred people selected Coke. Which of the following statements correctly describes how the confidence interval for the population proportion of people that prefer Coke should be computed?

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

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

Answer 2

Using the concept of confidence interval, the correct option is:

D. There are at least 15 successes and 15 failures. A large sample confidence interval for the population proportion can be computed by:

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

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:

• 200 people select coke, so 200 successes.
• 200 people did not select coke, so 200 failures.
• Thus, the correct option is D.

A similar problem is given at https://brainly.com/question/15224233