Respuesta :
The expected value is 160 and SE for the number of students in the sample is 9.78
a)Given: students of which 25000 of which 10000 are older than 25 and 25000-10000=15000 are not older than 25.
we represent 400 students by drawing 400 tickets from a box that contains 15000 tickets labeled 0 and 10000 tickets labeled 1
Expected value and standard deviation of a box:
First, we determine the expected value of the box, which is the sum of all values on the tickets by the number of tickets.
[tex]expected value box=\frac{15000*0+10000*1}{25000}\\\\ =\frac{10000}{25000} =\frac{2}{5}[/tex]
expected value box=0.4
let us next determine the standard deviation using the shortcut formula:
SD=(big number-small number)*√fraction with small number*fraction with a small number.
[tex]SD=(1-0)*\sqrt{\frac{10000}{25000} *\frac{15000}{25000} \\\\SD=1*\sqrt{\frac{2}{5} *\frac{3}{5} } \\SD=1*\sqrt{\frac{6}{25} } =\frac{\sqrt{6} }{5}[/tex]
SD=0.4899.
Expected value sum=Number of draws*expected value box
=400*0.4
Expected value sum=160
standard error of the sum is the product of the square root of the number of draws and the standard deviation of the box.
SE Sum=√number of draws*SD box
SE Sum=√400*0.4899
=20*0.4899
SE Sum=9.78
b)EXpected value and standard error:
The expected value of the percentage is the expected value of the sum divided by the number of draws.
Expected value percentage=Expected value sum/Number of draws*100%
160/400*100
=0.4*100%
Expected value percentage=400%
The standard error of the percentage is the standard error for the sum divided by the sample size:
SE%=SE for number/Number of draws*100%
=9.798/400*100%
=0.0245*100%
SE% =2.45%
To learn more about Expected value:
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