Chapter 4: Q. 95 (page 280)

Football on TVA Gallup poll conducted telephone interviews with a random sample of $1000$ adults aged $18$ and older. Of these, $37 %$ said that football was their favorite sport to watch on television. The margin of error for this estimate is $3.1$ percentage points.
a. Would you be surprised if a census revealed that $50 %$ of adults in the population would say their favorite sport to watch on TV is football? Explain your answer.
b. Explain how Gallup could decrease the margin of error

Short Answer

Expert verified

A.Yes, I would be surprised if a census revealed that $50 %$ of the population would say their favorite sport to watch on TV is football.

b.Gallup could decrease the margin of error by increasing the sample size.

Step by step solution

Part (a) Step 1: Given Information

We are given following information:

Total random samples (age $18$ and more) = $1000$

The total number of samples out of $1000$ whose favorite sport is football to watch on TV is $370$ .

The margin of error for this estimate is $3.1$ percentage points.

We need to explain will we be surprised if a census revealed that $50 %$ of the adult population would say their favorite sport to watch on TV is football.

Part (a) Step 2: Explanation

Yes, I would be surprised if a census revealed that $50 %$ of the population would say their favorite sport to watch on TV is football. Because we expect the parameter to fall within the range of $33.1 %$ to $40.1 %$ , a value of $50 %$ seems unlikely and unusual.