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:
<em>Perimeter of ABC = AB + BC+AC. Replace letters with equations.</em>
<em>3x^2-7x+2</em><em> = </em><u><em>2x^2-10x+6 + x^2-x-4 + AC</em></u><em> = </em><em>3x^2-11x+2 + AC</em><em>.</em>
<em>AC = 4x;</em>
Answer:
Step-by-step explanation:
denotes the set of elements in both A and C, which is
.
denotes the complement of set B, which is the set of all elements that are in the universal set that are not in set B. In this case, this set is ![\{3, 4, 5, 6, 8, 11, 13, 16, 17, 19, 20, 22, 23, 24, 25, 26, 27, 28\}](https://tex.z-dn.net/?f=%5C%7B3%2C%204%2C%205%2C%206%2C%208%2C%2011%2C%2013%2C%2016%2C%2017%2C%2019%2C%2020%2C%2022%2C%2023%2C%2024%2C%2025%2C%2026%2C%2027%2C%2028%5C%7D)
Answer:
2
Step-by-step explanation: