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 127 people living in Gastown and finds that 21 have an annual income that is below the poverty line.

Part i) The proportion of the 127 people who are living below the poverty line, 21/127, is a:

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

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

1)

Statistics are numbers that summarize data from a sample, i.e. some subset of the entire population.

Answer is statistic

2)

sample proportion, = 0.165354
sample size, n = 127
Standard error, SE = sqrt(pcap * (1 - pcap)/n)
SE = sqrt(0.165354 * (1 - 0.165354)/127) = 0.033

Given CI level is 95%, hence α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025, Zc = Z(α/2) = 1.96

Margin of Error, ME = zc * SE
ME = 1.96 * 0.033
ME = 0.0647

CI = (pcap - z*SE, pcap + z*SE)
CI = (0.165354 - 1.96 * 0.033 , 0.165354 + 1.96 * 0.033)
CI = (0.101 , 0.230)