Question

Houston TX has about twice as many residents as Dallas TX. A pollster took a random sample of 1000 residents of Dallas and asked them whether or not they favored more drilling for oil. If the same question were asked of residents of Houston, how many residents would the pollster need to randomly sample to have the same margin of error as the poll in Dallas? (Choose the option closest to the correct answer.)   

a. 1000 b. 500                          c. 2000

Answer 1

Here we are given that,

HoustonTX has about twice as many residents as Dallas TX.

Let N1 = Population Size of DallasTX

Then Population size of HoustonTX = 2* N1

A pollster took a random sample of 1000 residents of Dallas and asked them whether or not they favored more drilling for oil.

i.e. here, sample size for Dallas TX is

n1 = 1000

Further,we have to answer,

If the same question were asked of residents of Houston, how many residents would the pollster need to randomly sample to have the same margin of error as the poll in Dallas?

We have the following alternatives.

a. 1000 b. 500                          c. 2000

Notice that, Population of Houston is 2 times the Population of Dallas.

Hence, if a sample of n1= 1000 is selected for Dallas ,then

For Houston, the pollster should select a sample of size

2* n1

i.e. 2*1000 = 2000

Hence, for having the same margin of error, the pollster should select 2000 residents of Houston in sample.

Hence, Option C. 2000 is the correct alternative.

This answers your question.

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