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Chapter 4: Q. 95 (page 280)

Football on TVA Gallup poll conducted telephone interviews with a random sample of 1000adults aged 18and older. Of these, 37%said that football was their favorite sport to watch on television. The margin of error for this estimate is 3.1percentage 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

01

Part (a) Step 1: Given Information

We are given following information:

Total random samples (age 18and more) =1000

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

The margin of error for this estimate is 3.1percentage 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.

02

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%to40.1%, a value of 50%seems unlikely and unusual.

03

Part (b) Step  1: Given Information

We need to explain decrease of margin of error due to Gallup.

04

Part (b) Step 2: Explanation

Gallup could decrease the margin of error by increasing the sample sizes.

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