Question

1. A non-profit agency wants to estimate the proportion of adults who answer yes to the question, ‘Was there ever a time in your life when you did not have a place to live?' They want to estimate the percentage at the 95% level with a margin of error of nor more than 0.5%.

   1. Find a sample size that will guarantee their confidence interval will have a margin of error of less than 0.5%.

   2. Why is the sample size you found in part likely to be far bigger than necessary?

   3. To get a better estimate of the sample size they will need, they take a preliminary sample of 30 adults, of which 2 answered yes to the question. About what sample size should they realistically expect to need?

Answer 1

1.

2.

The sample size is so big because we are using the worst-case scenario proportion of 0.5.

3.

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