A survey research company uses random digit dialing. They have a contract, to es

Question

A survey research company uses random digit dialing. They have a contract, to estimate the percentage of people watching Spanish language television in several Southwestern cities. They took a sample of size 1,000 in Austin, Texas - which has about 600,000 residents. They are satisfied with the accuracy of the estimates for Austin.
Dallas has about twice the population of Austin, but similar demographics. True or false, and explain: to get about the same accuracy in Dallas as in Austin, the company should use a sample size of 2,000.

Explanation / Answer

False,

Company does not have to use sample size of 2000 to get the same accuracy, because both regions have same demograpics and sample size of 1000 is large enough. as population in both the cases is very large.

to justify this, as sample size increases t distribution approaches z distribution, and when sample size is above 1000 they are almost same... so it doesn't matter if sample size increases further in that... the accuracy level will be same

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