Question

A government official is in charge of allocating social programs throughout the city of Vancouver. He will decide where these social outreach programs should be located based on the percentage of residents living below the poverty line in each region of the city. He takes a simple random sample of 128 people living in Gastown and finds that 20 have an annual income that is below the poverty line.

Suppose that the government official wants to re-estimate the population proportion and wishes for his 95% confidence interval to have a margin of error no larger than 0.03. How large a sample should he take to achieve this? Please carry answers to at least six decimal places in intermediate steps.

Sample size =

Answer 1

Here

Now E=0.03

And z value is 1.96 as P(-1.96<z<1.96)=0.95

So we will find n using formula of E

Hence