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 124 people living in Gastown and finds that 25 have an annual income that is below the poverty line.

Part i) The proportion of the 124 people who are living below the poverty line, 25/124, is a:

A. statistic.
B. variable of interest.
C. parameter.

Part ii) Use the sample data to compute a 95% confidence interval for the true proportion of Gastown residents living below the poverty line.

(Please carry answers to at least six decimal places in intermediate steps. Give your final answer to the nearest three decimal places).

95% confidence interval = ( , )

Answer 1

Let p denotes the true proportion of Gastown residents living below the poverty line.

i) The proportion of the 124 people who are living below the poverty line, 25/124, is a: statistic, as this proportion is observed in a sample.

ii)