A government official is in charge of allocating social programs throughout the

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

Part i) The Wilson adjusted proportion of the 123 people who are living below the poverty line, (25+2)/(123+4), is a:

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

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.)

95% confidence interval

Explanation / Answer

a.
parameter

b. when conisder (25+2)/(123+4)
Plus Four Confidence Interval
CI = p ± Z a/2 Sqrt(p*(1-p)/n+4)))
x = Mean
n = Sample Size
a = 1 - (Confidence Level/100)
Za/2 = Z-table value
CI = Confidence Interval
Mean(x)=25
Sample Size(n)=123
Sample proportion = x+2/n+4 =0.212598
Confidence Interval = [ 0.212598 ±Z a/2 ( Sqrt ( 0.212598*0.787402) /127)]
= [ 0.212598 - 1.96* Sqrt(0.001318) , 0.2126 + 1.96* Sqrt(0.001318) ]
= [ 0.141439,0.283757]

When consider (25/123)
confidence interval = [ 0.203252 ± 1.96 * Sqrt ( (0.203252*0.796748) /123) ) ]
= [0.203252 - 1.96 * Sqrt ( (0.203252*0.796748) /123) , 0.203252 + 1.96 * Sqrt ( (0.203252*0.796748) /123) ]
= [0.132134 , 0.27437]

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