Question

In a Harris​ poll, adults were asked if they are in favor of abolishing the penny. Among the​ responses,1229 answered​ "no," 484 answered​ "yes," and 400 had no opinion. What is the sample proportion of yes​ responses, and what notation is used to represent​ it?A.p=0.229The symbol p is used to represent a sample proportion.B.^p=0.283.The symbol ^p is used to represent a sample proportion.C.^p=0.229The symbol p with caret<="">p is used to represent a sample proportion.D.p=0.283 The symbol p is used to represent a sample proportion.

Answer 1

C.^p=0.229The symbol p with caret<="">p is used to represent a sample proportion.

Explanation:

Data given

1229 people answered​ "no"

484 people answered​ "yes"

400 people had no opinion

The grand total is 1229+484+400=2113 people

Let p= true proportion of yes​ responses for the population

`\hat p` the proportion of yes estimated in th sample

Solution to the problem

The estimate population proportions is givn by the following formula:

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

Where X represent the people with a characteristic specified and n the sample size. For our case we have this:

`\hat p =(484)/(2113)=0.229`

If we analyze one by one the possible options we have this:

A.p=0.229 The symbol p is used to represent a sample proportion

False the estimated proportion
`\hat p` is not equal to the population proportion p

B.^p=0.283 The symbol ^p is used to represent a sample proportion.

False, the estimated proportion of yes was 0.229 not 0.283

C.^p=0.229 The symbol p with caret<="">p is used to represent a sample proportion.

True, the estimated proportion of yes is 0.229 and the correct way to express the estimation is
`\hat p`

D.p=0.283 The symbol p is used to represent a sample proportion.

False, the estimated proportion is 0.229 and not 0.283.