Question

In a Harris​ poll, adults were asked if they are in favor of abolishing the penny. Among the​ responses, 1241 answered​ "no," 459 answered​ "yes," and 352 had no opinion. What is the sample proportion of yes​ responses, and what notation is used to represent​ it? A.ModifyingAbove p with caret p=0.270. The symbol ModifyingAbove p with caret p is used to represent a sample proportion. B.p=0.224. The symbol p is used to represent a sample proportion. C.ModifyingAbove p with caret p=0.224. The symbol ModifyingAbove p with caret p is used to represent a sample proportion. D.p=0.270. The symbol p is used to represent a sample proportion.

Answer 1

C.ModifyingAbove p with caret p=0.224. The symbol ModifyingAbove p with caret p is used to represent a sample proportion.

Explanation:

Data given and notation

X= 459 represent the number of people that answer yes

1241 people answer no and 352 had no opinion

n= 459+1241+352=2052 represent the sampplpe size selected

Solution to the problem

What is the sample proportion of yes​ responses, and what notation is used to represent​ it?

If we want to find the sample proportion of yes we need to apply the following formula:

`\hat p =(X)/(n)`

Where X represent the number of people with the characteristic desired in the sample and n the sample size selected.

For this case we have:

`\hat p =(X)/(n)=(459)/(2052)=0.224`

Let's analyze the possible options given:

A.ModifyingAbove p with caret p=0.270. The symbol ModifyingAbove p with caret p is used to represent a sample proportion.

False the sample proportion is 0.224 not 0.270

B.p=0.224. The symbol p is used to represent a sample proportion.

The sample proportion is 0.224 not the population proportion for this case this statement is False.

C.ModifyingAbove p with caret p=0.224. The symbol ModifyingAbove p with caret p is used to represent a sample proportion.

Correct the
`\hat p= 0.224` represent th sample proportion and it's the correct way to express it.

D.p=0.270. The symbol p is used to represent a sample proportion.

False the sample proportion is 0.224 not 0.270