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Answer: a) Required minimum sample size= 219
b) Required minimum sample size= 271
Step-by-step explanation:
As per given , we have
Margin of error : E= 5% =0.05
Critical z-value for 90% confidence interval : ![z_{\alpha/2}=1.645](https://tex.z-dn.net/?f=z_%7B%5Calpha%2F2%7D%3D1.645)
a) Prior estimate of true proportion: p=28%=0.28
Formula to find the sample size :-
![n=p(1-p)(\dfrac{z_{\alpha/2}}{E})^2\\\\=0.28(1-0.28)(\dfrac{1.645}{0.05})^2\\\\=218.213856\approx219](https://tex.z-dn.net/?f=n%3Dp%281-p%29%28%5Cdfrac%7Bz_%7B%5Calpha%2F2%7D%7D%7BE%7D%29%5E2%5C%5C%5C%5C%3D0.28%281-0.28%29%28%5Cdfrac%7B1.645%7D%7B0.05%7D%29%5E2%5C%5C%5C%5C%3D218.213856%5Capprox219)
Required minimum sample size= 219
b) If no estimate of true proportion is given , then we assume p= 0.5
Formula to find the sample size :-
![n=0.5(1-0.5)(\dfrac{z_{\alpha/2}}{E})^2\\\\=0.25(\dfrac{1.645}{0.05})^2\\\\=270.6025\approx271](https://tex.z-dn.net/?f=n%3D0.5%281-0.5%29%28%5Cdfrac%7Bz_%7B%5Calpha%2F2%7D%7D%7BE%7D%29%5E2%5C%5C%5C%5C%3D0.25%28%5Cdfrac%7B1.645%7D%7B0.05%7D%29%5E2%5C%5C%5C%5C%3D270.6025%5Capprox271)
Required minimum sample size= 271
Answer:
B
Step-by-step explanation:
The sum of the 3 angles in a triangle = 180° , then
y + 10 + 2y + 50 = 180 , that is
3y + 60 = 180 ( subtract 60 from both sides )
3y = 120 ( divide both sides by 3 )
y = 40 → B
Answer:
Given the sequence 20, 24, 28, 32, 36, . . . find the 60th term.
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nth term pattern: a(n) = 20 + (n-1)4
60th term: a(60) = 20 + 59*4 = 256
Step-by-step explanation: