Question

In: Statistics and Probability

Suppose you’re hired by the government of Spain to estimate the proportion of residents who are...

Suppose you’re hired by the government of Spain to estimate the proportion of residents who are atheists. According to the guidelines, the estimate must have a margin of error no greater than 1% with 95% confidence.

How many people would you have to sample to ensure that you are within the guidelines?

Show a calculation to support your answer.

Expert Solution

Answer:

Given that,

Suppose you’re hired by the government of Spain to estimate the proportion of residents who are atheists.

According to the guidelines, the estimate must have a margin of error no greater than 1% with 95% confidence.

How many people would you have to sample to ensure that you are within the guidelines:

For 95% confidence level:

=1-0.95=0.05

/2=0.05/2=0.025

Then,

Z_/2=Z_0.025=1.96 (Since, from C.I table)

Given, Error (E)=1%=0.01

Let,

Therefore, the sample size is,

[Since, ]

Therefore, Number of people to sample=9604.

orchestra answered 2 years ago

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