Respuesta :
The percentage of households in the town with internet access is estimates as 47.8%, give or take 2.2% or so.
According to statement we have given
239 of the 500 households in the sample had internet access.
So, find sample percentage then
Sample percentage= 500/239 =0.478=47.8%
Thus we estimate the percentage as 47.8%.
The box contains 25,000 tickets of which 47.8% are 1's and the remaining 52.2% tickets are 0's. We will draw 500 tickets from the box.
Number of draws=500
Now, find the SD then
[tex]SD= (Big number - Small number) * \sqrt{Fraction with big number * fraction with small number}[/tex]
Substitute the values then
[tex]SD= (1 - 0) * \sqrt{0.478 *0.522}[/tex]
[tex]SD=0.4995[/tex]
Now find the standard error of sum then
The standard error of the sum is the product of the square root of the number of draws and the standard deviation of the box.
[tex]SE sum =\sqrt{Number of draws} * SD box[/tex]
[tex]SE sum =\sqrt{500} * 0.4995[/tex]
[tex]SE sum =11.16[/tex]
Now find the standard error of percentage then
The standard error of the percentage is the standard error for the sum divided by the sample size.
SE percentage= SE for number/Number of draws ×100%
= 50011.1692×100%
≈0.022×100%
=2.2%
Thus the percentage of households in the town with internet access is estimates as 47.8%, give or take 2.2% or so.
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