A randomized telephone survey of adults in the United States determines that a certain number out of 504 respondents have one or more pets. They use p^ to construct a 95% confidence interval to estimate the proportion p of American adults who have pets to be (0.56137,0.60529). How many respondents said they have one or more pets?
283
294
305
290

The critical value for 95% of confidence is

And since we know the total and the proportion is defined as:

If we solve for X (number of people who say yes) we got:

And the best answer would be:

294

Step-by-step explanation:

We know that the confidence interval for the proportion is given by:

The margin of error for the proportion interval is given by this formula:  

   (a)  

The margin of error can be calculated with this formula:

And the estimation for the true proportion is:

The critical value for 95% of confidence is

And since we know the total and the proportion is defined as:

If we solve for X (number of people who say yes) we got:

And the best answer would be:

294

it's equivalent, so we can say that its equal.

let's call the denominator x and the numerador is 18 less then denominator, x - 18.

multiply

2.x = 5.(x - 18)

2x = 5x - 90

90 = 5x - 2x

90 = 3x

x = 90/3

x = 30

so: